A349659 Sum of the nonrefactorable divisors of n.

0, 0, 3, 4, 5, 9, 7, 4, 3, 15, 11, 13, 13, 21, 23, 20, 17, 9, 19, 39, 31, 33, 23, 13, 30, 39, 30, 53, 29, 69, 31, 52, 47, 51, 47, 13, 37, 57, 55, 39, 41, 93, 43, 81, 68, 69, 47, 77, 56, 90, 71, 95, 53, 90, 71, 53, 79, 87, 59, 93, 61, 93, 94, 116, 83, 141, 67, 123, 95, 141, 71

Offset: 1

Author

Wesley Ivan Hurt, Nov 23 2021

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Refactorable Number

Crossrefs

Cf. A000203, A335182.

Programs

Mathematica

a[n_] := DivisorSum[n, # &, !Divisible[#, DivisorSigma[0, #]] &]; Array[a, 100] (* Amiram Eldar, Nov 24 2021 *)

PARI

a(n) = sumdiv(n, d, if (d%numdiv(d), d)); \\ Michel Marcus, Nov 24 2021

Formula

a(n) = A000203(n) - A335182(n).

a(p) = p for odd primes p. - Wesley Ivan Hurt, Nov 28 2021