A345284 - OEIS

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A345284

a(n) = Sum_{p|n} (p #).

0, 2, 6, 2, 30, 8, 210, 2, 6, 32, 2310, 8, 30030, 212, 36, 2, 510510, 8, 9699690, 32, 216, 2312, 223092870, 8, 30, 30032, 6, 212, 6469693230, 38, 200560490130, 2, 2316, 510512, 240, 8, 7420738134810, 9699692, 30036, 32, 304250263527210, 218, 13082761331670030, 2312, 36

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..45.

FORMULA

G.f.: Sum_{k>=1} prime(k)# * x^prime(k) / (1 - x^prime(k)). - Ilya Gutkovskiy, Sep 10 2021

a(prime(n)) = A002110(n). - Wesley Ivan Hurt, Oct 18 2021

EXAMPLE

a(14) = Sum_{p|14} p # = 2 # + 7 # = 2 + 7*5*3*2 = 212.

MATHEMATICA

Table[Sum[Product[i^(PrimePi[i] - PrimePi[i - 1]), {i, k}] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 60}]