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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

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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 *)