decagonal numbers

Decagonal numbers are figurate numbers of the form $n(4n-3)$

(see picture aside).

The sum of the reciprocals of decagonal numbers is $\pi/6+\log2$ .

The first decagonal numbers are 1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242, 1387, 1540, 1701, 1870 more terms

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here

A graph displaying how many decagonal numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.

Useful links Mathworld, Decagonal Number
Wikipedia, Decagonal number
OEIS, Sequence A001107

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

aban 10 27 52 + 997552000012 abundant 126 540 1242 + 49946022 Achilles 4000 469567 1026675 38637897507 admirable 3052 alternating 10 27 52 + 876589252 amenable 52 85 232 + 999650497 amicable 19552219155 apocalyptic 540 1105 1701 + 29326 arithmetic 27 85 126 + 9993501 astonishing 27 Bell 52 binomial 10 126 1540 + 2367195337045 brilliant 10 451 1387 + 990061957 c.decagonal 451 145351 46802701 + 4852597686751 c.heptagonal 19951 962851 16088702701 776445148501 c.nonagonal 10 1540 11935 + 18342198104230 c.pentagonal 109726 2164576 228160269751 4500937275451 c.square 85 1105 98125 + 150798234220045 c.triangular 10 85 976 + 864014364059701 cake 232 2626 Carmichael 1105 6601 748657 + 953828131201 congruent 52 85 126 + 9993501 constructible 10 85 cube 27 Cunningham 10 126 2047 cyclic 85 451 1105 + 9968227 d-powerful 175 370 2626 + 9457162 de Polignac 7267 9457 31417 + 99865045 deceptive 451 6601 14701 + 99654651601 deficient 10 27 52 + 9993501 dig.balanced 10 52 232 + 199692226 Duffinian 27 85 175 + 9968227 eban 52 4000 30066030 economical 10 27 175 + 19582837 emirpimes 85 1387 2047 + 98034751 equidigital 10 27 175 + 19582837 eRAP 255208612 esthetic 10 232 evil 10 27 85 + 999650497 Friedman 126 10251 32851 + 943326 frugal 1701 133407 469567 + 976515625 gapful 297 451 1540 + 99997143840 happy 10 637 2425 + 9980860 Harshad 10 27 126 + 9997050217 heptagonal 540 2887450 1123674201 6004054625647 hex 1387 42127 52204237 + 59665447746451 hexagonal 1540 1777555 2051297326 2367195337045 hoax 85 855 2232 + 99865045 iban 10 27 370 + 714447 idoneal 10 85 232 inconsummate 5076 10251 18837 + 990522 interprime 370 855 2835 + 99985000 Jacobsthal 85 junction 3510 12825 17226 + 99865045 Kaprekar 297 466830 katadrome 10 52 85 + 9850 Lehmer 85 451 1105 + 999890502997 lucky 297 451 855 + 9942985 Lynch-Bell 126 175 magic 175 1105 magnanimous 52 85 370 6601 metadrome 27 126 modest 151515 156222 500202 + 1540032670 Moran 27 370 1387 narcissistic 370 nialpdrome 10 52 85 + 99999985000000 nonagonal 1212751 977965238701 nude 126 175 2232 + 491741712 oban 10 27 85 + 976 octagonal 54405 2047494625 77055412679701 odious 52 370 451 + 999903451 palindromic 232 27972 76867 + 675972505279576 pancake 232 742 267547 + 411165133859452 panconsummate 10 85 pandigital 742 22275 124785 + 9576432810 partition 297 pentagonal 12376 118837251 1141075274626 pernicious 10 52 370 + 9993501 Perrin 10 persistent 1089346527 1632907485 1945802376 + 98941230675 plaindrome 27 126 1117777 Poulet 1105 1387 2047 + 999989162797327 power 27 powerful 27 4000 469567 + 38637897507 practical 126 540 1242 + 9880020 prim.abundant 1870 3052 297297 + 77673375 pseudoperfect 126 540 1242 + 998500 repfigit 742 repunit 85 2047 1307020 Rhonda 2835 Ruth-Aaron 126 370 26650 + 907239581326 self 637 5967 10660 + 999524032 semiprime 10 85 451 + 99945007 sliding 52 Smith 27 85 13747 + 99865045 sphenic 370 742 1105 + 99705217 star 14701 141164101 1355457688201 super Niven 10 540 4000 69300 super-d 2232 10660 14701 + 9955602 tau 232 2232 14220 + 997501680 taxicab 2837477081601 tetrahedral 10 1540 10660 triangular 10 1540 11935 + 18342198104230 trimorphic 3751 uban 10 27 52 + 36000087000052 Ulam 126 175 370 + 9729720 undulating 232 2626 151515 unprimeable 3052 5365 6930 + 9955602 untouchable 52 540 976 + 990522 vampire 12526290 1223547930 1319814405 + 4305885970 wasteful 52 85 126 + 9993501 weird 19390 Woodall 2047 Zuckerman 175 2232 1182112 + 7221312 Zumkeller 126 540 1242 + 96876 zygodrome 1117777 22994422 6663334455 + 880000077224422