OFFSET
1,4
COMMENTS
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
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-François Alcover, May 09 2017 *)
PROG
(PARI) a(n) = sumdiv(n, d, d*((d==1) || ispower(d))); \\ Michel Marcus, Oct 02 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Dec 15 2003
STATUS
approved