A350339 Sum of the nontrivial divisors of n that are the product of up to 3 (not necessarily distinct) primes.

0, 2, 3, 6, 5, 11, 7, 14, 12, 17, 11, 27, 13, 23, 23, 14, 17, 38, 19, 41, 31, 35, 23, 35, 30, 41, 39, 55, 29, 71, 31, 14, 47, 53, 47, 54, 37, 59, 55, 49, 41, 95, 43, 83, 77, 71, 47, 35, 56, 92, 71, 97, 53, 65, 71, 63, 79, 89, 59, 107, 61, 95, 103, 14, 83, 143, 67, 125, 95, 143

Offset

1,2

Comments

Sum of the 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

Table of n, a(n) for n=1..70.

Formula

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

Maple

f:= n -> convert(select(t -> numtheory:-bigomega(t)<=3, numtheory:-divisors(n)), `+`)-1:
map(f, [$1..100]); # Robert Israel, Dec 26 2021

Mathematica

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

Crossrefs

Cf. A001222 (Omega), A350338.

Sequence in context: A303695 A345321 A378545 * A039653 A335372 A106379

Adjacent sequences: A350336 A350337 A350338 * A350340 A350341 A350342

Keyword

nonn

Author

Wesley Ivan Hurt, Dec 25 2021

Status

approved