A174670 Divisors of the order of the Monster group.

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

Offset: 1

Author

Reinhard Zumkeller, Apr 02 2010

Keywords

• fini
• nonn
• easy

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).

Examples

			......... 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.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Sporadic Group
• Index entries for sequences related to divisors of numbers

Programs

PARI

divisors(808017424794512875886459904961710757005754368000000000)
\\ Warning: output is ~13 GB.
\\ Charles R Greathouse IV, Sep 02 2015