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A333644 a(n) = Sum_{k=1..n} floor(n/k) * prime(k). 0
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 (list; graph; refs; listen; history; text; internal format)
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

CROSSREFS

Cf. A000040, A024916, A333471.

Sequence in context: A194111 A102999 A225277 * A014112 A227016 A268347

Adjacent sequences:  A333641 A333642 A333643 * A333645 A333646 A333647

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 31 2020

STATUS

approved

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Last modified September 26 02:28 EDT 2020. Contains 337346 sequences. (Running on oeis4.)