A345263 a(n) = Sum_{d|n} d^rad(d).
1, 5, 28, 21, 3126, 46688, 823544, 85, 757, 10000003130, 285311670612, 3032688, 302875106592254, 11112006826381564, 437893890380862528, 341, 827240261886336764178, 34059641, 1978419655660313589123980, 10250000003146, 5842587018385982521381947992, 341427877364219557681958394200
Offset: 1
Keywords
Examples
a(4) = Sum_{d|4} d^rad(d) = 1^1 + 2^2 + 4^2 = 21.
a(6) = Sum_{d|6} d^rad(d) = 1^1 + 2^2 + 3^3 + 6^6 = 46688.
Programs
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Mathematica
Table[Sum[(1 - Ceiling[n/i] + Floor[n/i]) i^Product[k^((PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[i/k] + Floor[i/k])), {k, i}], {i, n}], {n, 30}] -
PARI
rad(n) = factorback(factorint(n)[, 1]); a(n) = sumdiv(n, d, d^rad(d)); \\ Michel Marcus, Jun 12 2021
Formula
a(prime(n)) = A125137(n). - Michel Marcus, Jun 12 2021
Comments