A377519 The number of divisors of n that are terms in A207481.

1, 2, 2, 3, 2, 4, 2, 3, 3, 4, 2, 6, 2, 4, 4, 3, 2, 6, 2, 6, 4, 4, 2, 6, 3, 4, 4, 6, 2, 8, 2, 3, 4, 4, 4, 9, 2, 4, 4, 6, 2, 8, 2, 6, 6, 4, 2, 6, 3, 6, 4, 6, 2, 8, 4, 6, 4, 4, 2, 12, 2, 4, 6, 3, 4, 8, 2, 6, 4, 8, 2, 9, 2, 4, 6, 6, 4, 8, 2, 6, 4, 4, 2, 12, 4, 4, 4

Offset

1,2

Comments

The sum of these divisors is A377520(n), and the largest of them is A377518(n).

Links

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

Formula

a(n) = A000005(A377518(n)).

Multiplicative with a(p^e) = min(p, e) + 1.

Dirichlet g.f.: zeta(s)^2 * Product_{p prime} (1 - 1/p^((p+1)*s)).

Mathematica

f[p_, e_] := Min[p, e] + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, min(f[i, 1], f[i, 2]) + 1); }

Crossrefs

Cf. A000005, A013661, A207481, A377516, A377518, A377520.

Sequence in context: A196437 A106491 A073184 * A073182 A282446 A049599

Adjacent sequences: A377516 A377517 A377518 * A377520 A377521 A377522

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 30 2024

Status

approved