A236286 - OEIS

%I #9 Jan 23 2014 00:19:36

%S 1,2,2,27,2,4096,2,16384,81,65536,2,2821109907456,2,1048576,262144,

%T 30517578125,2,21936950640377856,2,131621703842267136,4194304,

%U 268435456,2,324518553658426726783156020576256,729,4294967296,67108864,6140942214464815497216,2

%N a(n) = tau(n)^sigma(n) / tau(n)^n, where tau(n) = A000005(n) = the number of divisors of n and sigma(n) = A000203(n) = the sum of divisors of n.

%C a(n) = tau(n)^sigma_p(n), where sigma_p(n) = A001065(n) = the sum of proper divisors of n.

%H Jaroslav Krizek, <a href="/A236286/b236286.txt">Table of n, a(n) for n = 1..50</a>

%F a(n) = A236285(n) / A236284(n) = A000005(n)^A000203(n) / A000005(n)^n = A000005(n)^A001065(n).

%F a(p) = 2 for p = primes (A000040).

%e a(4) = tau(4)^sigma(4) / tau(4)^4 = 3^7 /3^4 = 27.

%t Table[DivisorSigma[0, n]^[DivisorSigma[1, n] - n], {n, 1000}]

%o (PARI) s=[]; for(n=1, 30, s=concat(s, sigma(n, 0)^sigma(n)/sigma(n, 0)^n)); s \\ _Colin Barker_, Jan 22 2014

%Y Cf. A000005 (tau(n)), A000203 (sigma(n)), A001065 (sigma_p(n)), A062758 (n^tau(n)), A217872 (sigma(n)^n), A236284 (tau(n)^n), A236285 (tau(n)^sigma(n)).

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Jan 21 2014