A365634 The number of divisors of n that are terms of A048102.

1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1

Offset

1,4

Links

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

Formula

Multiplicative with a(p^e) = 1 + [e = p], where [] is the Iverson bracket.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + (p-1)/p^(p+1)) = 1.153074089009... .

Mathematica

f[p_, e_] := If[e == p, 2, 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~, if(f[i, 2] == f[i, 1], 2, 1)); }

Crossrefs

Cf. A048102, A365632, A365635.

Sequence in context: A198293 A368330 A043281 * A320267 A304327 A307428

Adjacent sequences: A365631 A365632 A365633 * A365635 A365636 A365637

Keyword

nonn,easy,mult

Author

Amiram Eldar, Sep 14 2023

Status

approved