A224440 - OEIS

%I #10 Nov 12 2017 02:52:23

%S 1,3,16,343,1296,248832,262144,170859375,815730721,198359290368,

%T 61917364224,8293509467471872,56693912375296,876488338465357824,

%U 21035720123168587776,23465261991844685929951,121439531096594251776,1117116121846700839825703079,262144000000000000000000

%N a(n) = sigma(n)^(n-1).

%C Here sigma(n) = A000203(n) is the sum of the divisors of n.

%H Seiichi Manyama, <a href="/A224440/b224440.txt">Table of n, a(n) for n = 1..335</a>

%F Logarithmic derivative of A224439.

%e L.g.f.: L(x) = x + 3^1*x^2/2 + 4^2*x^3/3 + 7^3*x^4/4 + 6^4*x^5/5 + 12^5*x^6/6 +...

%e where exponentiation yields the g.f. of A224439:

%e exp(L(x)) = 1 + x + 2*x^2 + 7*x^3 + 93*x^4 + 357*x^5 + 41927*x^6 +...

%o (PARI) {a(n)=sigma(n)^(n-1)}

%o for(n=1, 20, print1(a(n), ", "))

%Y Cf. A224439, A217872.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Apr 06 2013

%E Offset corrected by _Seiichi Manyama_, Nov 10 2017