A369903 -id:A369903 - cp's OEIS frontend

A369740 a(n) = Sum_{p|n, p prime} p^sigma(n/p).

0, 2, 3, 8, 5, 43, 7, 128, 81, 189, 11, 6283, 13, 599, 1354, 32768, 17, 539633, 19, 340269, 8962, 5427, 23, 282784363, 15625, 18581, 1594323, 17600759, 29, 648338330, 31, 2147483648, 546082, 267057, 508274, 23426548268849, 37, 1055435, 4811530, 4428564089229, 41, 300565790978

Offset: 1

Wesley Ivan Hurt, Jan 30 2024

Cf. A000203 (sigma), A323599, A369903, A369904.

Table[DivisorSum[n, #^DivisorSigma[1, n/#] &, PrimeQ[#] &], {n, 50}]

a(p^k) = p^((1-p^k)/(1-p)) for p prime and k>=1. - Wesley Ivan Hurt, Jul 16 2025

A369904 a(n) = n * Sum_{p|n, p prime} sigma(n/p) / p.

Original entry on oeis.org

0, 1, 1, 6, 1, 18, 1, 28, 12, 36, 1, 100, 1, 62, 42, 120, 1, 189, 1, 208, 68, 138, 1, 456, 30, 188, 117, 364, 1, 612, 1, 496, 144, 312, 86, 1038, 1, 386, 194, 960, 1, 1080, 1, 820, 477, 558, 1, 1936, 56, 955, 318, 1120, 1, 1782, 162, 1688, 392, 876, 1, 3336, 1, 998, 789

Offset: 1

Wesley Ivan Hurt, Feb 05 2024

Cf. A000203 (sigma), A323599, A329354, A369740, A369903.

Table[n*DivisorSum[n, DivisorSigma[1, n/#]/# &, PrimeQ[#] &], {n, 100}]

a(p^k) = p^(k-1)*(p^k-1)/(p-1), for prime p and k >= 1. - Wesley Ivan Hurt, Jun 26 2024

cp's OEIS Frontend

A369740 a(n) = Sum_{p|n, p prime} p^sigma(n/p).

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