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 A174670 Divisors of the order of the Monster group. 9
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 75, 76, 77, 78, 80 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Let Mnr = A001228(26) = 808017424794512875886459904961710757005754368000000000, also called the Monster number, cf. A003131; the sequence is finite with A174601(26) = 424488960 terms; a(n) = n for n < 37 = A053669(Mnr) = (smallest prime not in A002267); 24 of the 26 terms of A001228 are divisors of Mnr, the exceptions are A001228(19) and A001228(23), orders of groups Ly and J4; also the first 36 factorials and the first 11 primorials are divisors of Mnr (cf. examples); A174671 gives divisors of Mnr sorted into decreasing order: A174671(n)=a(424488960-n+1)=Mnr/a(n). LINKS R. Zumkeller, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Sporadic Group EXAMPLE ......... a(30) = A002110(3) = ........... 30 = 5#; ........ a(101) = A000142(5) = .......... 120 = 5!; ........ a(159) = A002110(4) = .......... 210 = 7#; ........ a(398) = A000142(6) = .......... 720 = 6!; ........ a(888) = A002110(5) = ......... 2310 = 11#; ....... a(1461) = A000142(7) = ......... 5040 = 7!; ....... a(1931) = A001228(1) = ......... 7920; ....... a(4207) = A002110(6) = ........ 30030 = 13#; ....... a(4952) = A000142(8) = ........ 40320 = 8!; ....... a(7859) = A001228(2) = ........ 95040; ...... a(10787) = A001228(3) = ....... 175560; ...... a(15477) = A000142(9) = ....... 362880 = 9!; ...... a(17056) = A001228(4) = ....... 443520; ...... a(18257) = A002110(7) = ....... 510510 = 17#; ...... a(19792) = A001228(5) = ....... 604800; ...... a(44571) = A000142(10) = ..... 3628800 = 10!; ...... a(67510) = A002110(8) = ...... 9699690 = 19#; ...... a(68918) = A001228(6) = ..... 10200960; ..... a(118553) = A000142(11) = .... 39916800 = 11!; ..... a(123436) = A001228(7) = ..... 44352000; ..... a(129447) = A001228(8) = ..... 50232960; ..... a(223787) = A002110(9) = .... 223092870 = 23#; ..... a(231256) = A001228(9) = .... 244823040; ..... a(291999) = A000142(12) = ... 479001600 = 12!. ..... a(360936) = A001228(10) = ... 898128000; ..... a(584543) = A001228(11) = .. 4030387200; .. a(424488960) = A001228(26) = ......... Mnr, the last term. PROG (PARI) divisors(808017424794512875886459904961710757005754368000000000) \\ Warning: output is ~13 GB. \\ Charles R Greathouse IV, Sep 02 2015 CROSSREFS Sequence in context: A273886 A258068 A273885 * A212554 A178772 A296870 Adjacent sequences:  A174667 A174668 A174669 * A174671 A174672 A174673 KEYWORD fini,nonn,easy AUTHOR Reinhard Zumkeller, Apr 02 2010 STATUS approved

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Last modified April 22 10:58 EDT 2021. Contains 343174 sequences. (Running on oeis4.)