A133477 - OEIS

A133477

Sum of cubefree divisors of n excluding 1.

0, 2, 3, 6, 5, 11, 7, 6, 12, 17, 11, 27, 13, 23, 23, 6, 17, 38, 19, 41, 31, 35, 23, 27, 30, 41, 12, 55, 29, 71, 31, 6, 47, 53, 47, 90, 37, 59, 55, 41, 41, 95, 43, 83, 77, 71, 47, 27, 56, 92, 71, 97, 53, 38, 71, 55, 79, 89, 59, 167, 61, 95, 103, 6, 83, 143, 67, 125, 95, 143, 71, 90

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OFFSET

1,2

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A073185(n) - 1. - N. J. A. Sloane, Nov 30 2007

EXAMPLE

a(8) = 6 because the divisors of 8 are {1,2,4,8}, the cubefree divisors are 1, 2, 4 so we get a(8) = 2 + 4 = 6.

MATHEMATICA

scfd[n_]:=Total[Select[Divisors[n], Max[Transpose[FactorInteger[#]][[2]]]<3&]]; Array[scfd, 80]-1 (* Harvey P. Dale, Nov 30 2014 *)

f[p_, e_] := 1 + p + If[e > 1, p^2, 0]; a[1] = 0; a[n_] := -1 + Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jul 09 2022 *)