A350338 Number of nontrivial divisors of n that are the product of up to 3 (not necessarily distinct) primes.

0, 1, 1, 2, 1, 3, 1, 3, 2, 3, 1, 5, 1, 3, 3, 3, 1, 5, 1, 5, 3, 3, 1, 6, 2, 3, 3, 5, 1, 7, 1, 3, 3, 3, 3, 7, 1, 3, 3, 6, 1, 7, 1, 5, 5, 3, 1, 6, 2, 5, 3, 5, 1, 6, 3, 6, 3, 3, 1, 10, 1, 3, 5, 3, 3, 7, 1, 5, 3, 7, 1, 8, 1, 3, 5, 5, 3, 7, 1, 6, 3, 3, 1, 10, 3, 3, 3, 6, 1, 10, 3

Offset

1,4

Comments

Number of divisors of n of the form p, p^2, p*q, p^3, p^2*q, or p*q*r where p,q,r are primes.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from exponents in factorization of n

Formula

a(n) = Sum_{d|n} Sum_{k=1..3} [Omega(d) = k], where [ ] is the Iverson bracket.

Mathematica

a[n_] := DivisorSum[n, 1 &, 0 < PrimeOmega[#] <= 3 &]; Array[a, 100] (* Amiram Eldar, Dec 26 2021 *)

Prog

(PARI) A350338(n) = sumdiv(n, d, (d>1)*(bigomega(d)<=3)); \\ Antti Karttunen, Nov 02 2022

Crossrefs

Cf. A001222 (Omega), A350331.

Sequence in context: A079167 A304793 A199570 * A239707 A294928 A325770

Adjacent sequences: A350335 A350336 A350337 * A350339 A350340 A350341

Keyword

nonn

Author

Wesley Ivan Hurt, Dec 25 2021

Status

approved