A333644 a(n) = Sum_{k=1..n} floor(n/k) * prime(k).

2, 7, 14, 26, 39, 62, 81, 112, 142, 187, 220, 287, 330, 395, 460, 544, 605, 712, 781, 904, 1001, 1116, 1201, 1376, 1486, 1633, 1766, 1945, 2056, 2279, 2408, 2623, 2798, 3001, 3180, 3482, 3641, 3876, 4091, 4406, 4587, 4924, 5117, 5432, 5717, 6004, 6217, 6668, 6914, 7285

Offset

1,1

Comments

Partial sums of A007445.

Links

Table of n, a(n) for n=1..50.

Formula

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

Mathematica

Table[Sum[Floor[n/k] Prime[k], {k, n}], {n, 50}]

Prog

(PARI) a(n) = sum(k=1, n, (n\k)*prime(k)); \\ Michel Marcus, Mar 31 2020
(Python)
from sympy import prime
def A333644(n): return sum(prime(k)*(n//k) for k in range(1, n+1)) # Chai Wah Wu, Jun 24 2026

Crossrefs

Cf. A000040, A007445, A024916, A333471.

Sequence in context: A102999 A225277 A367954 * A374236 A014112 A227016

Adjacent sequences: A333641 A333642 A333643 * A333645 A333646 A333647

Keyword

nonn,changed

Author

Ilya Gutkovskiy, Mar 31 2020

Status

approved