A377381 a(n) is the number of divisors of n that are interprime numbers (A024675).

0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 3, 0, 0, 1, 1, 0, 3, 0, 1, 1, 0, 0, 3, 0, 1, 1, 1, 0, 3, 0, 1, 0, 1, 0, 5, 0, 0, 1, 1, 0, 3, 0, 1, 3, 0, 0, 3, 0, 1, 0, 2, 0, 3, 0, 2, 0, 0, 0, 6, 0, 0, 2, 2, 0, 1, 0, 2, 1, 0, 0, 6, 0, 0, 1, 2, 0, 3, 0, 1, 2, 0, 0, 5, 0, 1, 0

Offset: 1

Author

Marius A. Burtea, Dec 05 2024

Keywords

• nonn

Examples

			Because A024675(1) = 4 it follows that a(1) = a(2) = a(3) = 0 and a(4) = 1.
a(12) = 3 because it has the divisors 4 = A024675(1), 6 = A024675(2) and 12 = A024675(4).
		

Crossrefs

Cf. A024675.

Programs

Magma

ipr:=func ;[#[d:d in Divisors(n)|ipr(d)]:n in [1..100]];

Mathematica

a[n_] := DivisorSum[n, 1 &, CompositeQ[#] && NextPrime[#] + NextPrime[#, -1] == 2*# &]; Array[a, 100] (* Amiram Eldar, Dec 11 2024 *)