A377516 The number of divisors of n that are terms in A276078.

1, 2, 2, 2, 2, 4, 2, 2, 3, 4, 2, 4, 2, 4, 4, 2, 2, 6, 2, 4, 4, 4, 2, 4, 3, 4, 3, 4, 2, 8, 2, 2, 4, 4, 4, 6, 2, 4, 4, 4, 2, 8, 2, 4, 6, 4, 2, 4, 3, 6, 4, 4, 2, 6, 4, 4, 4, 4, 2, 8, 2, 4, 6, 2, 4, 8, 2, 4, 4, 8, 2, 6, 2, 4, 6, 4, 4, 8, 2, 4, 3, 4, 2, 8, 4, 4, 4

Offset

1,2

Comments

The sum of these divisors is A377517(n), and the largest of them is A377515(n).

Links

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

Formula

a(n) = A000005(A377515(n)).

Multiplicative with a(p^e) = min(pi(p), e) + 1, where pi(n) = A000720(n).

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

Mathematica

f[p_, e_] := Min[PrimePi[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(primepi(f[i, 1]), f[i, 2]) + 1); }

Crossrefs

Cf. A000005, A000720, A013661, A276078, A377515, A377517, A377519.

Sequence in context: A023157 A228849 A359541 * A069733 A187467 A081755

Adjacent sequences: A377513 A377514 A377515 * A377517 A377518 A377519

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 30 2024

Status

approved