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D-numbers
Also known as 3-Knödel numbers, they are number  $n>3$  such that  $n$  divides  $k^{n-2}-k$  for all  $1<k<n$  relatively prime to  $n$.

For example, 9 is a D-number since it divides all the numbers  $2^7-2$,  $4^7-4$,  $5^7-5$,  $7^7-7$  and  $8^7-8$.

The smallest 3 × 3 magic square whose entries are D-numbers is

8726769
123141159
21315195

Below, the spiral pattern of D-numbers up to  $100^2$. See the page on prime numbers for an explanation and links to similar pictures.

spiral pattern of D-numbers

The first D-numbers are 9, 15, 21, 33, 39, 51, 57, 63, 69, 87, 93, 111, 123, 129, 141, 159, 177, 183, 195, 201, 213, 219 more terms

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

aban 15 21 33 39 + 7000989 abundant 4095 16695 1527435 2475795 + 6310395 admirable 4095 alternating 21 63 69 87 + 7038723 amenable 21 33 57 69 + 7043133 apocalyptic 411 669 693 723 + 29919 arithmetic 15 21 33 39 + 7043133 astonishing 15 Bell 15 betrothed 195 binomial 15 21 1953 3003 + 5572791 brilliant 15 21 c.pentagonal 51 141 681 951 + 7018251 cake 15 93 congruent 15 21 39 63 + 7043133 constructible 15 51 771 196611 Cullen 2049 Cunningham 15 33 63 129 + 7011903 Curzon 21 33 69 141 + 7042569 cyclic 15 33 51 69 + 7043109 d-powerful 63 267 849 2283 + 7040589 de Polignac 7431 8031 11541 17229 + 7042281 deficient 15 21 33 39 + 7043133 dig.balanced 15 21 141 177 + 7043079 double fact. 15 Duffinian 21 39 57 63 + 7043133 economical 15 21 111 123 + 2999949 emirpimes 15 39 51 93 + 7042731 equidigital 15 21 111 123 + 2999949 esthetic 21 87 123 321 + 5454321 Eulerian 57 1191 4083 evil 15 33 39 51 + 7043133 fibodiv 183 2733 3903 9267 + 4788039 Fibonacci 21 Friedman 15567 15627 16347 16743 + 995331 gapful 195 315 693 1443 + 6999363 happy 129 219 291 921 + 7042773 Harshad 21 63 111 195 + 6727539 heptagonal 21483 hexagonal 15 3003 hoax 24963 178923 226083 334971 + 3827043 Hogben 21 57 111 183 + 6993381 house 933 7617 hyperperfect 21 iban 21 111 123 141 + 777477 iccanobiF 39 idoneal 15 21 33 57 + 177 inconsummate 63 195 381 411 + 999993 insolite 111 interprime 15 21 39 69 + 7042323 Jacobsthal 21 junction 111 303 309 315 + 7042227 katadrome 21 51 63 87 + 987621 Lehmer 15 51 771 196611 Leyland 57 177 131361 423393 lonely 31431 370317 Lucas 123 843 271443 lucky 15 21 33 51 + 7043109 Lynch-Bell 15 315 1935 magic 15 111 magnanimous 21 metadrome 15 39 57 69 + 2346789 modest 39 69 111 309 + 7023333 Moran 21 63 111 195 + 2000001 Motzkin 21 51 853467 nialpdrome 21 33 51 63 + 6666531 nonagonal 111 nude 15 33 111 315 + 3313131 oban 15 33 39 57 + 993 octagonal 21 odious 21 69 87 93 + 7042881 palindromic 33 111 141 303 + 7023207 panconsummate 15 21 39 57 + 267 pandigital 15 21 141 177 + 799899 partition 15 pentagonal 51 pernicious 21 33 69 87 + 7042881 Perrin 39 51 1497 1983 + 2240877 plaindrome 15 33 39 57 + 6667779 prim.abundant 4095 16695 Proth 33 57 129 177 + 6987777 pseudoperfect 4095 16695 repdigit 33 111 repfigit 7647 repunit 15 21 57 63 + 6993381 Ruth-Aaron 15 1683 8463 1040403 Sastry 183 self 411 501 591 681 + 7042773 semiprime 15 21 33 39 + 7043133 Smith 1935 24963 178923 226083 + 2215983 sphenic 195 399 1023 1443 + 7011903 straight-line 111 123 159 321 + 876543 strobogrammatic 69 111 6009 68889 + 6911169 super-d 69 219 339 381 + 7042881 tetranacci 15 10671 283953 triangular 15 21 1953 3003 + 5572791 trimorphic 51 249 501 5001 + 500001 uban 15 21 33 39 + 7000041 Ulam 57 69 87 177 + 7042683 undulating 141 303 393 717 + 3737373 unprimeable 10815 188235 1527435 1700415 + 6340995 upside-down 159 753 951 112899 + 994611 wasteful 33 39 51 57 + 7043133 Wieferich 3279 10533 Woodall 63 159 1023 10239 Zuckerman 15 111 315 13113 Zumkeller 4095 16695 zygodrome 33 111 11199 22233 + 6666999