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A165797 a(n) = n^( sigma(n) - tau(n) ). 1

%I #9 Feb 27 2014 06:16:29

%S 1,2,9,256,625,1679616,117649,8589934592,3486784401,100000000000000,

%T 25937424601,552061438912436417593344,23298085122481,

%U 83668255425284801560576,332525673007965087890625

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

%C The power of n with exponent given by the difference between its sum of divisors and its count of divisors.

%H Jaroslav Krizek, <a href="/A165797/b165797.txt">Table of n, a(n) for n = 1..50</a>

%F a(n) = n^(A000203(n)-A000005(n)) = n^A000203(n) / n^A000005(n) = n^A065608(n).

%F a(n) = A100879(n) / A062758(n).

%F a(p) = p^(p-1) for p = prime.

%e a(4) = 4^(sigma(4)-tau(4)) = 4^(7-3) = 4^4 = 256.

%t Table[n^[ DivisorSigma[1, n] - DivisorSigma[0, n]], {n, 50}]

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Sep 27 2009

%E Slightly edited by _R. J. Mathar_, Sep 29 2009

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)