A383769 -id:A383769 - cp's OEIS frontend

A383768 Numerators of the sequence whose Dirichlet convolution with itself yields cubes (A000578).

1, 4, 27, 24, 125, 54, 343, 160, 2187, 250, 1331, 324, 2197, 686, 3375, 1120, 4913, 2187, 6859, 1500, 9261, 2662, 12167, 2160, 46875, 4394, 98415, 4116, 24389, 3375, 29791, 8064, 35937, 9826, 42875, 6561, 50653, 13718, 59319, 10000, 68921, 9261, 79507, 15972, 273375

Offset: 1

Vaclav Kotesovec, May 09 2025

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
Vaclav Kotesovec, Graph - the asymptotic ratio (10000 terms)

Cf. A000578, A299149, A299150, A318649, A318512, A383769 (denominators).

for(n=1, 100, print1(numerator(direuler(p=2, n, 1/(1-p^3*X)^(1/2))[n]), ", "))

Sum_{k=1..n} A383768(k) / A383769(k) ~ n^4/(4*sqrt(Pi*log(n))) * (1 + (1-2*gamma)/(8*log(n))), where gamma is the Euler-Mascheroni constant A001620.

A383791 Numerators of the sequence whose Dirichlet convolution with itself yields fourth powers (A000583).

Original entry on oeis.org

1, 8, 81, 96, 625, 324, 2401, 1280, 19683, 2500, 14641, 3888, 28561, 9604, 50625, 17920, 83521, 19683, 130321, 30000, 194481, 58564, 279841, 51840, 1171875, 114244, 2657205, 115248, 707281, 101250, 923521, 258048, 1185921, 334084, 1500625, 236196, 1874161, 521284, 2313441

Offset: 1

Vaclav Kotesovec, May 10 2025

Numerators of Dirichlet g.f.: Sum_{n>=1} a(n)/n^s = zeta(s-4)^(1/2).

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
Vaclav Kotesovec, Graph - the asymptotic ratio (10000 terms)

Cf. A000583, A383792 (denominators).

Cf. A299149, A299150, A318649, A318512, A383768, A383769.

for(n=1, 100, print1(numerator(direuler(p=2, n, 1/(1-p^4*X)^(1/2))[n]), ", "))

Sum_{k=1..n} A383791(k) / A383792(k) ~ n^5 / (5*sqrt(Pi*log(n))) * (1 + (1/5 - gamma/2)/(2*log(n))), where gamma is the Euler-Mascheroni constant A001620.

A383792 Denominators of the sequence whose Dirichlet convolution with itself yields fourth powers (A000583).

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 2, 1, 8, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 8, 1, 16, 1, 2, 1, 2, 1, 4, 1, 4, 1, 2, 1, 4, 1, 2, 1, 2, 1, 16, 1, 2, 1, 8, 1, 4, 1, 2, 2, 4, 1, 4, 1, 2, 1, 2, 1, 16, 1, 4, 1, 2, 1, 4, 1, 2, 1, 2, 1, 16, 1, 4, 1, 2, 1, 128, 1, 2, 1, 4

Offset: 1

Vaclav Kotesovec, May 10 2025

Denominators of Dirichlet g.f.: Sum_{n>=1} a(n)/n^s = zeta(s-4)^(1/2).

First differs from A318658 at n = 54.

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Cf. A000583, A318658, A383791 (numerators).

Cf. A299149, A299150, A318649, A318512, A383768, A383769.

for(n=1, 100, print1(denominator(direuler(p=2, n, 1/(1-p^4*X)^(1/2))[n]), ", "))

cp's OEIS Frontend

A383768 Numerators of the sequence whose Dirichlet convolution with itself yields cubes (A000578).

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A383791 Numerators of the sequence whose Dirichlet convolution with itself yields fourth powers (A000583).

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PARI

Formula

A383792 Denominators of the sequence whose Dirichlet convolution with itself yields fourth powers (A000583).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI