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

Author

Vaclav Kotesovec, May 09 2025

Keywords

• nonn
• frac

Links

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

Crossrefs

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

Programs

PARI

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

Formula

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.