A350338 - OEIS

%I #9 Nov 02 2022 20:35:48

%S 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,

%T 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,

%U 3,7,1,8,1,3,5,5,3,7,1,6,3,3,1,10,3,3,3,6,1,10,3

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

%C 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.

%H Antti Karttunen, <a href="/A350338/b350338.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

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

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

%o (PARI) A350338(n) = sumdiv(n,d,(d>1)*(bigomega(d)<=3)); \\ _Antti Karttunen_, Nov 02 2022

%Y Cf. A001222 (Omega), A350331.

%K nonn

%O 1,4

%A _Wesley Ivan Hurt_, Dec 25 2021