A366969 a(n) = Sum_{k=3..n} (k-2) * floor(n/k).

0, 0, 1, 3, 6, 11, 16, 24, 32, 43, 52, 69, 80, 97, 114, 136, 151, 179, 196, 227, 252, 281, 302, 347, 373, 408, 441, 486, 513, 570, 599, 651, 692, 739, 780, 854, 889, 942, 991, 1066, 1105, 1186, 1227, 1300, 1367, 1432, 1477, 1582, 1634, 1716, 1781, 1868, 1919, 2024

Offset

1,4

Links

Table of n, a(n) for n=1..54.

Formula

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

a(n) = n + A024916(n) - 2*A006218(n). - Chai Wah Wu, Oct 30 2023

Prog

(PARI) a(n) = sum(k=3, n, (k-2)*(n\k));
(Python)
from math import isqrt
def A366969(n): return n+(-(s:=isqrt(n))*(s*(s-2)-7)+sum(((q:=n//w)+1)*(q+(w<<1)-8) for w in range(1, s+1))>>1) # Chai Wah Wu, Oct 30 2023

Crossrefs

Partial sums of A152771.

Cf. A006218, A024916, A366968, A366970, A366971.

Sequence in context: A278100 A087099 A181947 * A075703 A267583 A364198

Adjacent sequences: A366966 A366967 A366968 * A366970 A366971 A366972

Keyword

nonn

Author

Seiichi Manyama, Oct 30 2023

Status

approved