A323599 -id:A323599 - cp's OEIS frontend

A329371 Dirichlet convolution of the identity function with A246277.

0, 1, 1, 4, 1, 8, 1, 12, 5, 12, 1, 28, 1, 16, 11, 32, 1, 37, 1, 44, 15, 24, 1, 80, 7, 28, 19, 60, 1, 82, 1, 80, 21, 36, 15, 128, 1, 40, 27, 128, 1, 114, 1, 92, 49, 48, 1, 208, 9, 89, 33, 108, 1, 146, 21, 176, 39, 60, 1, 284, 1, 64, 69, 192, 25, 174, 1, 140, 45, 170, 1, 364, 1, 76, 70, 156, 21, 210, 1, 336, 65, 84, 1, 396, 33, 88, 55, 272, 1, 368, 25, 188, 63

Offset: 1

Antti Karttunen, Nov 12 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences computed from indices in prime factorization

Cf. A246277.

Cf. also A305796, A323599, A329347, A329372, A329373.

A246277(n) = if(1==n, 0, my(f = factor(n), k = primepi(f[1,1])-1); for (i=1, #f~, f[i,1] = prime(primepi(f[i,1])-k)); factorback(f)/2);
A329371(n) = sumdiv(n,d,(n/d)*A246277(d));

a(n) = Sum_{d|n} d * A246277(n/d).

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

Original entry on oeis.org

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

A369903 a(n) = Sum_{p|n, p prime} n^sigma(n/p).

Original entry on oeis.org

0, 2, 3, 64, 5, 1512, 7, 2097152, 6561, 1001000, 11, 8916136280064, 13, 1475791800, 11441250, 1152921504606846976, 17, 21979796247097344, 19, 262144000000001280000000, 37823053842, 12855002631059864, 23, 442501521100279866178075737690262732800, 244140625

Offset: 1

Wesley Ivan Hurt, Feb 05 2024

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

Table[DivisorSum[n, n^DivisorSigma[1, n/#] &, PrimeQ[#] &], {n, 30}]

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

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

A329371 Dirichlet convolution of the identity function with A246277.

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

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A369903 a(n) = Sum_{p|n, p prime} n^sigma(n/p).

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

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