A366984 - OEIS

A366984

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

3, 12, 25, 49, 73, 120, 159, 228, 296, 392, 473, 626, 734, 899, 1069, 1291, 1465, 1757, 1970, 2312, 2614, 2977, 3280, 3803, 4178, 4670, 5144, 5759, 6227, 6993, 7524, 8307, 8993, 9803, 10529, 11630, 12374, 13373, 14311, 15559, 16465, 17867, 18860, 20273, 21579, 23016

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..46.

FORMULA

G.f.: 1/(1-x) * Sum_{k>0} (1/(1-x^k)^3 - 1) = 1/(1-x) * Sum_{k>0} binomial(k+2,2) * x^k/(1-x^k).

PROG

(PARI) a(n) = sum(k=1, n, binomial(k+2, 2)*(n\k));

(Python)

from math import isqrt

def A366984(n): return (-(s:=isqrt(n))*(s*(s*(s+7)+17)+17)+sum(((q:=n//w)+1)*(q*(q+5)+3*(w*(w+3)+4)) for w in range(1, s+1)))//6 # Chai Wah Wu, Oct 31 2023

CROSSREFS

Partial sums of A363628.

Cf. A006218, A366983, A366985.

Cf. A366967.

Sequence in context: A331241 A068967 A071355 * A237650 A199242 A326725

Adjacent sequences: A366981 A366982 A366983 * A366985 A366986 A366987

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Oct 30 2023

STATUS

approved