A350331 Number of divisors of n that are prime or the product of 2 (not necessarily distinct) primes.

0, 1, 1, 2, 1, 3, 1, 2, 2, 3, 1, 4, 1, 3, 3, 2, 1, 4, 1, 4, 3, 3, 1, 4, 2, 3, 2, 4, 1, 6, 1, 2, 3, 3, 3, 5, 1, 3, 3, 4, 1, 6, 1, 4, 4, 3, 1, 4, 2, 4, 3, 4, 1, 4, 3, 4, 3, 3, 1, 7, 1, 3, 4, 2, 3, 6, 1, 4, 3, 6, 1, 5, 1, 3, 4, 4, 3, 6, 1, 4, 2, 3, 1, 7, 3, 3, 3, 4, 1, 7, 3, 4

Offset

1,4

Comments

Number of divisors of n of the form p, p^2, or p*q, where p and q are prime.

Links

Table of n, a(n) for n=1..92.

Formula

a(n) = A001221(n) + A086971(n).

Mathematica

a[1] = 0; a[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Total[Min[#, 2] & /@ e] + Binomial[Length[e], 2]]; Array[a, 100] (* Amiram Eldar, Dec 25 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, isprime(d) || (bigomega(d)==2)); \\ Michel Marcus, Dec 25 2021

Crossrefs

Cf. A000005 (tau), A001221 (omega), A086971.

Sequence in context: A323014 A385113 A391024 * A293227 A291208 A241165

Adjacent sequences: A350328 A350329 A350330 * A350332 A350333 A350334

Keyword

nonn

Author

Wesley Ivan Hurt, Dec 25 2021

Status

approved