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hoax numbers
A composite number the sum of whose digits is equal to the sum of the digits of its distinct prime factors is called hoax number.

For example,  $5464=2^3\cdot683$  is a hoax number since  $5+4+6+4=2+6+8+3$.

The first pair, triple, etc. of consecutive hoax numbers starts at 84, 12955, 291090, 9538589, 3541285143, 136063250955, and 253282144742, respectively.

Up to  $10^8$  there are 3183722 hoax numbers.

The smallest primitive Pythagorean triangle with 3 hoax sides is (32880, 4369, 33169).

Note that Smith numbers are defined similarly, but they take into account prime factors multiplicity. Clearly, a squarefree Smith number is also a hoax number.

The smallest 3 × 3 magic square whose entries are hoax numbers is

20252694
166274382
45422346

Below, the spiral pattern of hoax numbers up to  $80^2$. See the page on prime numbers for an explanation and links to similar pictures.

spiral pattern of hoax numbers

The first hoax numbers are 22, 58, 84, 85, 94, 136, 160, 166, 202, 234, 250, 265, 274, 308, 319, 336, 346, 355 more terms

Hoax numbers can also be... (you may click on names or numbers and on + to get more values)

ABA 160 2500 3042 + 98140050 aban 22 58 84 + 99000985 abundant 84 160 234 + 49999292 Achilles 16000 25000 39200 + 95520600 admirable 84 234 308 + 99994614 alternating 58 85 94 + 98987212 amenable 84 85 136 + 99999332 amicable 2924 69615 180848 + 84591405 apocalyptic 355 361 382 + 29938 arithmetic 22 85 94 + 9999895 astonishing 133533 178623 betrothed 507759 549219 1057595 + 84854315 binomial 84 136 364 + 99793128 brilliant 319 361 391 + 97333987 c.decagonal 361 9031 30811 + 98323951 c.heptagonal 22 3046 13672 + 99599116 c.nonagonal 136 11476 12880 + 99003556 c.octagonal 361 2401 39601 + 90611361 c.pentagonal 391 456 526 + 98486131 c.square 85 265 2965 + 97482685 c.triangular 85 136 166 + 99621526 cake 2325 32568 50184 + 82173826 Carmichael 656601 27336673 37167361 93614521 congruent 22 84 85 + 9999895 constructible 85 136 160 + 53478192 Cunningham 483 17575 24963 + 99820080 Curzon 438 645 650 + 99996146 cyclic 85 265 319 + 9999895 D-number 24963 178923 226083 + 3827043 d-powerful 1255 2064 2227 + 9992722 de Polignac 3505 4855 8023 + 99993307 decagonal 85 855 2232 + 99865045 deceptive 8149 226273 642001 + 98269633 deficient 22 58 85 + 9999922 dig.balanced 166 202 308 + 95581084 Duffinian 85 265 319 + 9999355 eban 2064 4054 6054 + 66066032 economical 160 166 250 + 19999858 emirpimes 58 85 94 + 99999238 enlightened 250 2500 25000 + 25000000 equidigital 160 166 250 + 19999858 eRAP 680350 1730404 3246724 + 96954909 esthetic 234 454 456 + 76545654 Eulerian 152637 evil 58 85 136 + 99999706 fibodiv 1822 6178 22117 + 70224572 Fibonacci 1346269 Friedman 1255 2500 10192 + 983445 frugal 2401 10240 10375 + 99601831 gapful 160 660 1111 + 99992520 Gilda 364 660 happy 94 319 391 + 9999355 harmonic 50401728 Harshad 84 234 308 + 99996350 heptagonal 1404 2356 2839 + 99814924 hex 5544721 6872047 31076227 + 93057991 hexagonal 861 9180 11476 + 99793128 Hogben 44733 190533 198471 + 99351057 house 18148 165425 258477 + 83980587 hyperperfect 4013833 8883841 14489437 + 79001833 iban 22 202 274 + 777417 idoneal 22 58 85 inconsummate 84 438 476 + 999860 interprime 160 274 483 + 99999058 Jacobsthal 85 junction 202 319 517 + 99999150 Kaprekar 851851 25252525 katadrome 84 85 94 + 9876210 Lehmer 85 1111 4369 + 99264451 lonely 1344 370316 4652428 47326803 Lucas 7881196 lucky 319 361 391 + 9998311 Lynch-Bell 735 1824 18624 + 2937816 magic 27455 143781 578865 + 93574910 magnanimous 58 85 94 + 66886483 metadrome 58 136 234 + 12456789 modest 627 654 1111 + 99818181 Moran 84 516 645 + 99957093 narcissistic 1741725 24678050 nialpdrome 22 84 85 + 99999650 nonagonal 6364 16975 17964 + 95027796 nude 22 336 424 + 99991332 O'Halloran 84 660 oban 58 85 308 + 985 octagonal 645 2640 35425 + 98452865 odious 22 84 94 + 99999332 palindromic 22 202 424 + 98122189 pancake 22 562 4279 + 99200656 panconsummate 85 166 361 pandigital 2826 2902 8415 + 95581084 partition 22 627 1255 + 8118264 pentagonal 22 2625 4676 + 99923285 pernicious 22 84 94 + 9999895 Perrin 22 644 plaindrome 22 58 136 + 66677788 Poulet 645 4369 13747 + 97863529 power 361 1600 2401 + 91011600 powerful 361 1600 2401 + 95520600 practical 84 160 234 + 9999150 prim.abundant 308 364 438 + 99994614 pronic 650 702 2352 + 99830072 Proth 1665 1921 2625 + 99581953 pseudoperfect 84 160 234 + 999860 repdigit 22 1111 6666666 repfigit 34348 86935 repunit 85 364 1111 + 99351057 Rhonda 47265 56356 733125 + 91485531 Ruth-Aaron 948 4191 43680 + 99360350 Saint-Exupery 55080 419580 440640 + 55080000 Sastry 22145328 self 424 861 1111 + 99997915 self-describing 22 15173331 17153133 + 33322828 semiprime 22 58 85 + 99999706 sliding 250 650 2500 + 78500000 Smith 22 58 85 + 99999706 sphenic 438 483 627 + 99997305 square 361 1600 2401 + 91011600 star 1633 16537 43861 + 98925961 straight-line 234 456 654 + 6666666 strobogrammatic 1111 9116 168891 + 96111196 subfactorial 265 super Niven 660 2640 6060 + 96300000 super-d 319 336 454 + 9999895 tau 84 136 424 + 99995120 taxicab 515375 1080891 1533357 + 54267003 tetrahedral 84 364 26235 + 91558740 tetranacci 2872 triangular 136 861 4656 + 99793128 tribonacci 274 2555757 uban 22 58 85 + 99000083 Ulam 319 382 456 + 9997800 undulating 202 424 454 + 25252525 unprimeable 516 535 895 + 9999895 untouchable 336 516 562 + 999860 upside-down 456 654 45556 + 99682411 vampire 117067 124483 136525 + 94765918 wasteful 22 58 84 + 9999922 weird 83312 338572 475684 + 927124 Wieferich 2685501 Woodall 895 Zeisel 44544219 Zuckerman 735 1111 1116 + 93112416 Zumkeller 84 160 234 + 99860 zygodrome 22 1111 3344 + 99991155