A174601 Numbers of divisors of orders of sporadic simple groups.

60, 112, 128, 192, 192, 384, 480, 384, 704, 896, 1056, 1920, 2688, 3200, 2816, 4256, 4320, 5880, 16128, 16896, 25536, 26400, 45056, 143616, 1580544, 424488960

Offset

1,1

Links

Table of n, a(n) for n=1..26.

Eric Weisstein's World of Mathematics, Sporadic Group

Index entries for sequences related to groups

Formula

a(n) = A000005(A001228(n)).

Example

a(1) = A000005(7920) = A000005(2^4 * 3^2 * 5^1 * 11^1) = (4+1)*(2+1)*(1+1)*(1+1) = 60;
a(26) = Product_{k>0} (A051161(k)+1) = (46+1)*(20+1)*(9+1)*(6+1)*(2+1)*(3+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(0+1)*(1+1)*(0+1)*(1+1)*(0+1)*(1+1)*(0+1)*(0+1)*(1+1)*(0+1)*(0+1)*... = 47*21*10*7*3*4*2*2*2*2*2*1*2*1*2*1*2*1*1*2*1*1*... = 424488960.

Mathematica

DivisorSigma[0, Sort[Array[FiniteGroupData[{"SporadicGroup", #}, "Order"] &, 26]]] (* Paolo Xausa, May 07 2026 *)

Crossrefs

Cf. A174670, A395630.

Cf. A000005, A001228.

Sequence in context: A217738 A351548 A182683 * A306908 A252961 A252962

Adjacent sequences: A174598 A174599 A174600 * A174602 A174603 A174604

Keyword

fini,full,nonn

Author

Reinhard Zumkeller, Apr 02 2010

Status

approved