A372836 a(n) is the numerator of Sum_{d|n, 1 < d < n} 1/d.

0, 0, 0, 1, 0, 5, 0, 3, 1, 7, 0, 5, 0, 9, 8, 7, 0, 10, 0, 21, 10, 13, 0, 35, 1, 15, 4, 27, 0, 41, 0, 15, 14, 19, 12, 3, 0, 21, 16, 49, 0, 53, 0, 39, 32, 25, 0, 25, 1, 21, 20, 45, 0, 65, 16, 9, 22, 31, 0, 107, 0, 33, 40, 31, 18, 7, 0, 57, 26, 73, 0, 61, 0, 39, 16, 63, 18, 89, 0, 21

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

Numerators of coefficients in expansion of Sum_{k>=2} x^(2*k) / (k * (1 - x^k)).

Example

0, 0, 0, 1/2, 0, 5/6, 0, 3/4, 1/3, 7/10, 0, 5/4, 0, 9/14, 8/15, 7/8, 0, 10/9, ...

Mathematica

nmax = 80; CoefficientList[Series[Sum[x^(2 k)/(k (1 - x^k)), {k, 2, nmax}], {x, 0, nmax}], x] // Numerator // Rest

Prog

(PARI) a(n) = numerator(sumdiv(n, d, if ((d>1) && (d<n), 1/d))); \\ Michel Marcus, May 14 2024

Crossrefs

Cf. A017665, A048050, A277790, A277791.

Sequence in context: A176867 A351208 A229175 * A326188 A201524 A230438

Adjacent sequences: A372833 A372834 A372835 * A372837 A372838 A372839

Keyword

nonn,frac

Author

Ilya Gutkovskiy, May 14 2024

Status

approved