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A062796 Inverse Moebius transform of f(n) = n^n (A000312). 24
1, 5, 28, 261, 3126, 46688, 823544, 16777477, 387420517, 10000003130, 285311670612, 8916100495200, 302875106592254, 11112006826381564, 437893890380862528, 18446744073726329093, 827240261886336764178, 39346408075296925042601, 1978419655660313589123980 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..386 (first 200 terms from Nick Hobson)

FORMULA

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

G.f.: Sum_{n>=1} n^n * x^n/(1 - x^n). - Paul D. Hanna, Oct 27 2009

Logarithmic derivative of A023879. - Paul D. Hanna, Sep 05 2012

EXAMPLE

n=6: divisors = {1,2,3,6}; 1^1 + 2^2 + 3^3 + 6^6 = 1 + 4 + 27 + 46656 = 46688 = a(6).

MATHEMATICA

a[n_] := DivisorSum[n, #^# &]; Array[a, 19] (* Jean-François Alcover, Dec 23 2015 *)

PROG

(PARI) vector(17, n, sumdiv(n, d, d^d))

(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

(PARI) a(n) = sumdiv(n, d, d^d ); \\ Joerg Arndt, Apr 14 2013

CROSSREFS

Cf. A000312, A023879.

Sequence in context: A116977 A238981 A163694 * A343573 A342677 A224607

Adjacent sequences:  A062793 A062794 A062795 * A062797 A062798 A062799

KEYWORD

nonn

AUTHOR

Labos Elemer, Jul 19 2001

STATUS

approved

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Last modified June 20 14:11 EDT 2021. Contains 345165 sequences. (Running on oeis4.)