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A062796 Inverse Moebius transform of f(n) = n^n (A000312).

%I A062796 #33 Jun 19 2022 15:23:21
%S A062796 1,5,28,261,3126,46688,823544,16777477,387420517,10000003130,
%T A062796 285311670612,8916100495200,302875106592254,11112006826381564,
%U A062796 437893890380862528,18446744073726329093,827240261886336764178,39346408075296925042601,1978419655660313589123980
%N A062796 Inverse Moebius transform of f(n) = n^n (A000312).
%H A062796 Seiichi Manyama, <a href="/A062796/b062796.txt">Table of n, a(n) for n = 1..386</a> (first 200 terms from Nick Hobson)
%F A062796 a(n) = Sum_{d|n} d^d.
%F A062796 G.f.: Sum_{n>=1} n^n * x^n/(1 - x^n). - _Paul D. Hanna_, Oct 27 2009
%F A062796 Logarithmic derivative of A023879. - _Paul D. Hanna_, Sep 05 2012
%e A062796 n=6: divisors = {1,2,3,6}; 1^1 + 2^2 + 3^3 + 6^6 = 1 + 4 + 27 + 46656 = 46688 = a(6).
%t A062796 a[n_] := DivisorSum[n, #^# &]; Array[a, 19] (* _Jean-François Alcover_, Dec 23 2015 *)
%o A062796 (PARI) vector(17, n, sumdiv(n, d, d^d))
%o A062796 (PARI) {a(n)=polcoeff(sum(m=1,n,m^m*x^m/(1-x^m +x*O(x^n))),n)} \\ _Paul D. Hanna_, Oct 27 2009
%o A062796 (PARI) a(n) = sumdiv(n,d, d^d ); \\ _Joerg Arndt_, Apr 14 2013
%o A062796 (Python)
%o A062796 from sympy import divisors
%o A062796 def A062796(n): return sum(d**d for d in divisors(n,generator=True)) # _Chai Wah Wu_, Jun 19 2022
%Y A062796 Cf. A000312, A023879.
%K A062796 nonn
%O A062796 1,2
%A A062796 _Labos Elemer_, Jul 19 2001