A367866 a(n) = Sum_{d|n} d * sigma(d) * mu(d)^2.
1, 7, 13, 7, 31, 91, 57, 7, 13, 217, 133, 91, 183, 399, 403, 7, 307, 91, 381, 217, 741, 931, 553, 91, 31, 1281, 13, 399, 871, 2821, 993, 7, 1729, 2149, 1767, 91, 1407, 2667, 2379, 217, 1723, 5187, 1893, 931, 403, 3871, 2257, 91, 57, 217, 3991, 1281, 2863, 91
Offset: 1
Links
- N. J. A. Sloane, Transforms.
Programs
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Mathematica
Table[Sum[d*DivisorSigma[1, d]*MoebiusMu[d]^2, {d, Divisors[n]}], {n, 100}] -
PARI
a(n) = sumdiv(n, d, if (issquarefree(d), d*sigma(d))); \\ Michel Marcus, Dec 04 2023
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Python
from math import prod from sympy import primefactors def A367866(n): return prod(p*(p+1)+1 for p in primefactors(n)) # Chai Wah Wu, Dec 05 2023
Formula
Multiplicative with a(p^e) = p^2 + p + 1. - Amiram Eldar, Dec 04 2023
Sum_{k=1..n} a(k) ~ n^3/3. - Vaclav Kotesovec, Dec 05 2023
Comments