cp's OEIS Frontend

A174601 Numbers of divisors of orders of sporadic simple groups.

%I A174601 #3 Feb 16 2025 08:33:12
%S A174601 60,112,128,192,192,384,480,384,704,896,1056,1920,2688,3200,2816,4256,
%T A174601 4320,5880,16128,16896,25536,26400,45056,143616,1580544,424488960
%N A174601 Numbers of divisors of orders of sporadic simple groups.
%C A174601 a(n) = A000005(A001228(n)).
%H A174601 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SporadicGroup.html">Sporadic Group</a>
%e A174601 a(1) = A000005(7920) = A000005(2^4 * 3^2 * 5^1 * 11^1) = (4+1)*(2+1)*(1+1)*(1+1) = 60;
%e A174601 a(26) = PROD((A051161(k)+1): k>0) = (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.
%Y A174601 Cf. A174670.
%K A174601 fini,full,nonn
%O A174601 1,1
%A A174601 _Reinhard Zumkeller_, Apr 02 2010