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A347405
a(n) = Sum_{d|n} 2^(tau(d) - 1).
4
1, 3, 3, 7, 3, 13, 3, 15, 7, 13, 3, 49, 3, 13, 13, 31, 3, 49, 3, 49, 13, 13, 3, 185, 7, 13, 15, 49, 3, 159, 3, 63, 13, 13, 13, 341, 3, 13, 13, 185, 3, 159, 3, 49, 49, 13, 3, 713, 7, 49, 13, 49, 3, 185, 13, 185, 13, 13, 3, 2275, 3, 13, 49, 127, 13, 159, 3, 49, 13, 159, 3, 2525, 3, 13, 49, 49
OFFSET
1,2
LINKS
FORMULA
If p is prime, a(p^n) = 2^(n+1) - 1.
G.f.: Sum_{k>=1} 2^(tau(k) - 1) * x^k/(1 - x^k).
MATHEMATICA
a[n_] := DivisorSum[n, 2^(DivisorSigma[0, #] - 1) &]; Array[a, 80] (* Amiram Eldar, Oct 08 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, 2^(numdiv(d)-1));
(PARI) my(N=99, x='x+O('x^N)); Vec(sum(k=1, N, 2^(numdiv(k)-1)*x^k/(1-x^k)))
CROSSREFS
Sequence in context: A119347 A323774 A062402 * A294015 A156838 A274845
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 08 2021
STATUS
approved