cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A307653 a(n) = Sum_{d|n} mu(d) * d^d.

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%I A307653 #28 Apr 22 2019 13:52:36
%S A307653 1,-3,-26,-3,-3124,46626,-823542,-3,-26,9999996872,-285311670610,
%T A307653 46626,-302875106592252,11112006824734470,437893890380856224,-3,
%U A307653 -827240261886336764176,46626,-1978419655660313589123978,9999996872,5842587018385982521380300852
%N A307653 a(n) = Sum_{d|n} mu(d) * d^d.
%H A307653 Seiichi Manyama, <a href="/A307653/b307653.txt">Table of n, a(n) for n = 1..388</a>
%F A307653 a(prime(n)^m) = 1 - prime(n)^prime(n) = -A088730(n) for m > 0.
%F A307653 G.f.: Sum_{k>=1} mu(k)*k^k*x^k/(1 - x^k). - _Ilya Gutkovskiy_, Apr 20 2019
%e A307653 a(6) = 1 - 2^2 - 3^3 + 6^6 = 46626.
%t A307653 Array[DivisorSum[#, MoebiusMu[#]*#^# &] &, 21] (* _Michael De Vlieger_, Apr 21 2019 *)
%o A307653 (PARI) {a(n) = sumdiv(n, d, moebius(d)*d^d)}
%Y A307653 Cf. A000040, A008683, A023900, A088730, A307654, A321222.
%K A307653 sign
%O A307653 1,2
%A A307653 _Seiichi Manyama_, Apr 20 2019