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

Offset: 1

Author

Jonathan Vos Post, Nov 29 2007

Keywords

• easy
• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A004709, A005117, A039653, A048250, A068318, A083681.

Cf. A073184, A073185.

Programs

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 *)

Formula

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

Extensions

Edited by N. J. A. Sloane, Nov 30 2007