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A327669
Sum of divisors of n that have an odd number of distinct prime factors.
2
0, 2, 3, 6, 5, 5, 7, 14, 12, 7, 11, 9, 13, 9, 8, 30, 17, 14, 19, 11, 10, 13, 23, 17, 30, 15, 39, 13, 29, 40, 31, 62, 14, 19, 12, 18, 37, 21, 16, 19, 41, 54, 43, 17, 17, 25, 47, 33, 56, 32, 20, 19, 53, 41, 16, 21, 22, 31, 59, 104, 61, 33, 19, 126, 18, 82, 67, 23, 26, 84
OFFSET
1,2
LINKS
FORMULA
G.f.: Sum_{k>=1} A030230(k) * x^A030230(k) / (1 - x^A030230(k)).
L.g.f.: log(B(x)) = Sum_{n>=1} a(n) * x^n / n, where B(x) = g.f. of A285799.
a(n) = Sum_{d|n} d * A092248(d).
a(n) = A000203(n) - A327670(n).
a(p) = p, where p is prime.
MAPLE
with(numtheory):
a:= n-> add(`if`(nops(factorset(d))::odd, d, 0), d=divisors(n)):
seq(a(n), n=1..80); # Alois P. Heinz, Sep 21 2019
MATHEMATICA
a[n_] := DivisorSum[n, # &, OddQ[PrimeNu[#]] &]; Table[a[n], {n, 1, 70}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 21 2019
STATUS
approved