A319072 a(n) is the sum of the non-bi-unitary divisors of n.

0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 8, 0, 0, 0, 4, 0, 9, 0, 12, 0, 0, 0, 0, 5, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 24, 18, 0, 0, 16, 7, 15, 0, 28, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 24, 8, 0, 0, 0, 36, 0, 0, 0, 45, 0, 0, 20, 40, 0, 0, 0, 24, 9, 0, 0, 64, 0, 0, 0, 0, 0, 54, 0, 48, 0, 0, 0, 0, 0, 21, 36, 87

Offset: 1

Author

Omar E. Pol, Sep 22 2018

Keywords

• nonn

Examples

			For n = 12 the divisors of 12 are 1, 2, 3, 4, 6, 12, and the bi-unitary divisors of 12 are 1, 3, 4, 12, hence the non-bi-unitary divisors of 12 are 2 and 6, and the sum of them is 2 + 6 = 8, so a(12) = 8. Also the sum of the divisors of 12 is 28, and the sum of the bi-unitary divisors of 12 is 20, so a(12) = 28 - 20 = 8.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A027750, A188999, A222266.

Programs

Mathematica

f1[p_, e_] := (p^(e+1) - 1)/(p - 1); f2[p_, e_] := f1[p, e] - If[OddQ[e], 0, p^(e/2)]; a[1] = 0; a[n_] := Times @@ f1 @@@ (fct = FactorInteger[n]) - Times @@ f2 @@@ fct; Array[a, 100] (* Amiram Eldar, Apr 04 2024 *)

Formula

a(n) = A000203(n) - A188999(n).