A358077 Sum of the nonprime divisors of n whose divisor complement is squarefree.

1, 1, 1, 4, 1, 7, 1, 12, 9, 11, 1, 22, 1, 15, 16, 24, 1, 33, 1, 34, 22, 23, 1, 48, 25, 27, 36, 46, 1, 62, 1, 48, 34, 35, 36, 72, 1, 39, 40, 72, 1, 84, 1, 70, 69, 47, 1, 96, 49, 85, 52, 82, 1, 108, 56, 96, 58, 59, 1, 142, 1, 63, 93, 96, 66, 128, 1, 106, 70, 130, 1, 144, 1, 75

Offset: 1

Author

Wesley Ivan Hurt, Oct 29 2022

Keywords

• nonn

Examples

			a(8) = 12. The nonprime divisors of 8 whose divisor complements are squarefree are 4 and 8 and their sum is 12.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A005117, A284118.

Programs

Mathematica

a[n_] := DivisorSum[n, # &, ! PrimeQ[#] && SquareFreeQ[n/#] &]; Array[a, 100] (* Amiram Eldar, Oct 30 2022 *)

PARI

a(n) = sumdiv(n, d, if (!isprime(d) && issquarefree(n/d), d)); \\ Michel Marcus, Oct 30 2022

Formula

a(n) = Sum_{d|n, nonprime d, n/d squarefree} d.