A373968 a(n) is the number of divisors of n that are Duffinian numbers (A003624).

0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 3, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 2, 1, 0, 0, 0, 4, 0, 0, 1, 3, 0, 0, 1, 2, 0, 1, 0, 1, 1, 0, 0, 3, 1, 2, 0, 1, 0, 2, 1, 2, 1, 0, 0, 1, 0, 0, 3, 5, 1, 0, 0, 1, 0, 1, 0, 4, 0, 0, 2, 1, 1, 1, 0, 3, 3, 0, 0, 2, 1, 0, 0, 2

Offset

1,8

Links

Table of n, a(n) for n=1..88.

Formula

a(p^k)) = k - 1, for p prime and k >= 1.

Example

Since A003624(1) = 4 then a(1) = a(2) = a(3) = 0 and a(4) = 1.
a(8) = 2 because 8 has the divisors 4 = A003624(1) and 8 = A003624(2).

Mathematica

a[n_] := DivisorSum[n, 1 &, CompositeQ[#] && CoprimeQ[#, DivisorSigma[1, #]] &]; Array[a, 100] (* Amiram Eldar, Jul 19 2024 *)

Prog

(Magma) f:=func<n|n ne 1 and not IsPrime(n) and Gcd(n, DivisorSigma(1, n)) eq 1>; [#[d:d in Divisors(k)|f(d)]:k in [1..100]];

Crossrefs

Cf. A000203, A003624, A009194.

Sequence in context: A046660 A368251 A183094 * A324192 A108730 A056973

Adjacent sequences: A373965 A373966 A373967 * A373969 A373970 A373971

Keyword

nonn

Author

Marius A. Burtea, Jul 12 2024

Status

approved