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

1,12

Links

Table of n, a(n) for n=1..87.

Example

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).

Mathematica

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

Prog

(Magma) ipr:=func<n|n ge 3 and not IsPrime(n) and 2*n eq NextPrime(n)+PreviousPrime(n)> ; [#[d:d in Divisors(n)|ipr(d)]:n in [1..100]];

Crossrefs

Cf. A024675.

Sequence in context: A359270 A318508 A100655 * A262262 A079275 A236314

Adjacent sequences: A377378 A377379 A377380 * A377382 A377383 A377384

Keyword

nonn

Author

Marius A. Burtea, Dec 05 2024

Status

approved