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

Author

Reinhard Zumkeller, Apr 02 2010

Keywords

• fini
• full
• nonn

Comments

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

Examples

			a(1) = A000005(7920) = A000005(2^4 * 3^2 * 5^1 * 11^1) = (4+1)*(2+1)*(1+1)*(1+1) = 60;
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.
		

Links

• Eric Weisstein's World of Mathematics, Sporadic Group

Crossrefs

Cf. A174670.