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A091051 Sum of divisors of n that are perfect powers. 5
1, 1, 1, 5, 1, 1, 1, 13, 10, 1, 1, 5, 1, 1, 1, 29, 1, 10, 1, 5, 1, 1, 1, 13, 26, 1, 37, 5, 1, 1, 1, 61, 1, 1, 1, 50, 1, 1, 1, 13, 1, 1, 1, 5, 10, 1, 1, 29, 50, 26, 1, 5, 1, 37, 1, 13, 1, 1, 1, 5, 1, 1, 10, 125, 1, 1, 1, 5, 1, 1, 1, 58, 1, 1, 26, 5, 1, 1, 1, 29, 118, 1, 1, 5, 1, 1, 1, 13, 1, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n) = 1 iff n is squarefree: a(A005117(n))=1, a(A013929(n))>1;

a(p^k) = 1+(p^2)*(p^(k-1)-1)/(p-1) for p prime, k>0.

a(A000961(n)) = A086455(n)-A025473(n).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16385

Eric Weisstein's World of Mathematics, Perfect Power

Eric Weisstein's World of Mathematics, Divisor Function

Index entries for sequences related to sums of divisors

FORMULA

G.f.: Sum_{k=i^j, i>=1, j>=2, excluding duplicates} k*x^k/(1 - x^k). - Ilya Gutkovskiy, Mar 20 2017

EXAMPLE

Divisors of n=108: {1,2,3,4,6,9,12,18,27,36,54,108}, a(108) = 1^2 + 2^2 + 3^2 + 3^3 + 6^2 = 1+4+9+27+36 = 77.

MATHEMATICA

a[n_] := DivisorSum[n, #*Boole[# == 1 || GCD @@ FactorInteger[#][[All, 2]] > 1]&]; Array[a, 90] (* Jean-Fran├žois Alcover, May 09 2017 *)

PROG

(PARI) a(n) = sumdiv(n, d, d*((d==1) || ispower(d))); \\ Michel Marcus, Oct 02 2014

CROSSREFS

Cf. A091050, A001597, A000203, A183104.

Differs from A183097 for the first time at n=72.

Sequence in context: A204007 A242404 A145295 * A183097 A285486 A230368

Adjacent sequences:  A091048 A091049 A091050 * A091052 A091053 A091054

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Dec 15 2003

STATUS

approved

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Last modified June 25 10:46 EDT 2019. Contains 324351 sequences. (Running on oeis4.)