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A350339 Sum of the nontrivial divisors of n that are the product of up to 3 (not necessarily distinct) primes. 0
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 (list; graph; refs; listen; history; text; internal format)
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
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: A133477 A303695 A345321 * A039653 A335372 A106379
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Dec 25 2021
STATUS
approved

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Last modified July 21 06:08 EDT 2024. Contains 374463 sequences. (Running on oeis4.)