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A174670 Divisors of the order of the Monster group.

%I A174670 #14 Feb 16 2025 08:33:12
%S A174670 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,
%T A174670 27,28,29,30,31,32,33,34,35,36,38,39,40,41,42,44,45,46,47,48,49,50,51,
%U A174670 52,54,55,56,57,58,59,60,62,63,64,65,66,68,69,70,71,72,75,76,77,78,80
%N A174670 Divisors of the order of the Monster group.
%C A174670 Let Mnr = A001228(26) = 808017424794512875886459904961710757005754368000000000, also called the Monster number, cf. A003131;
%C A174670 the sequence is finite with A174601(26) = 424488960 terms;
%C A174670 a(n) = n for n < 37 = A053669(Mnr) = (smallest prime not in A002267);
%C A174670 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;
%C A174670 also the first 36 factorials and the first 11 primorials are divisors of Mnr (cf. examples);
%C A174670 A174671 gives divisors of Mnr sorted into decreasing order: A174671(n)=a(424488960-n+1)=Mnr/a(n).
%H A174670 Reinhard Zumkeller, <a href="/A174670/b174670.txt">Table of n, a(n) for n = 1..10000</a>
%H A174670 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MonsterGroup.html">Sporadic Group</a>
%H A174670 <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>
%e A174670 ......... a(30) = A002110(3) = ........... 30 = 5#;
%e A174670 ........ a(101) = A000142(5) = .......... 120 = 5!;
%e A174670 ........ a(159) = A002110(4) = .......... 210 = 7#;
%e A174670 ........ a(398) = A000142(6) = .......... 720 = 6!;
%e A174670 ........ a(888) = A002110(5) = ......... 2310 = 11#;
%e A174670 ....... a(1461) = A000142(7) = ......... 5040 = 7!;
%e A174670 ....... a(1931) = A001228(1) = ......... 7920;
%e A174670 ....... a(4207) = A002110(6) = ........ 30030 = 13#;
%e A174670 ....... a(4952) = A000142(8) = ........ 40320 = 8!;
%e A174670 ....... a(7859) = A001228(2) = ........ 95040;
%e A174670 ...... a(10787) = A001228(3) = ....... 175560;
%e A174670 ...... a(15477) = A000142(9) = ....... 362880 = 9!;
%e A174670 ...... a(17056) = A001228(4) = ....... 443520;
%e A174670 ...... a(18257) = A002110(7) = ....... 510510 = 17#;
%e A174670 ...... a(19792) = A001228(5) = ....... 604800;
%e A174670 ...... a(44571) = A000142(10) = ..... 3628800 = 10!;
%e A174670 ...... a(67510) = A002110(8) = ...... 9699690 = 19#;
%e A174670 ...... a(68918) = A001228(6) = ..... 10200960;
%e A174670 ..... a(118553) = A000142(11) = .... 39916800 = 11!;
%e A174670 ..... a(123436) = A001228(7) = ..... 44352000;
%e A174670 ..... a(129447) = A001228(8) = ..... 50232960;
%e A174670 ..... a(223787) = A002110(9) = .... 223092870 = 23#;
%e A174670 ..... a(231256) = A001228(9) = .... 244823040;
%e A174670 ..... a(291999) = A000142(12) = ... 479001600 = 12!.
%e A174670 ..... a(360936) = A001228(10) = ... 898128000;
%e A174670 ..... a(584543) = A001228(11) = .. 4030387200;
%e A174670 .. a(424488960) = A001228(26) = ......... Mnr, the last term.
%o A174670 (PARI) divisors(808017424794512875886459904961710757005754368000000000)
%o A174670 \\ Warning: output is ~13 GB.
%o A174670 \\ _Charles R Greathouse IV_, Sep 02 2015
%K A174670 fini,nonn,easy
%O A174670 1,2
%A A174670 _Reinhard Zumkeller_, Apr 02 2010