A366723 a(n) = Sum_{k=1..n} (-1)^(k-1) * binomial(floor(n/k)+4,5).

1, 5, 21, 50, 121, 236, 447, 736, 1247, 1896, 2898, 4151, 5972, 8146, 11292, 14797, 19643, 25248, 32564, 40663, 51515, 63168, 78119, 94452, 114998, 136933, 164849, 193753, 229714, 268334, 314711, 362824, 422746, 483950, 558046, 635070, 726461, 820420, 934186, 1048245

Offset

1,2

Links

Table of n, a(n) for n=1..40.

Formula

a(n) = Sum_{k=1..n} binomial(k+3,4) * (floor(n/k) mod 2).

G.f.: -1/(1-x) * Sum_{k>=1} (-x)^k/(1-x^k)^5 = 1/(1-x) * Sum_{k>=1} binomial(k+3,4) * x^k/(1+x^k).

Prog

(PARI) a(n) = sum(k=1, n, (-1)^(k-1)*binomial(n\k+4, 5));
(Python)
from math import comb
def A366723(n):
    c, j = 0, 1
    while j <= n:
        k = n//j
        m = n//k
        if m-j&1^1:
            c += (comb(k+4, 5) if j&1 else -comb(k+4, 5))
        j = m+1
    return c # Chai Wah Wu, May 18 2026

Crossrefs

Partial sums of A366814.

Cf. A078471, A366395, A366659.

Cf. A365439.

Sequence in context: A201279 A146721 A099979 * A039659 A147238 A316435

Adjacent sequences: A366720 A366721 A366722 * A366724 A366725 A366726

Keyword

nonn

Author

Seiichi Manyama, Oct 24 2023

Status

approved