A345284 - OEIS

%I #10 Oct 18 2021 19:31:26

%S 0,2,6,2,30,8,210,2,6,32,2310,8,30030,212,36,2,510510,8,9699690,32,

%T 216,2312,223092870,8,30,30032,6,212,6469693230,38,200560490130,2,

%U 2316,510512,240,8,7420738134810,9699692,30036,32,304250263527210,218,13082761331670030,2312,36

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

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

%F a(prime(n)) = A002110(n). - _Wesley Ivan Hurt_, Oct 18 2021

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

%t 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}]

%Y Cf. A002110, A062797.

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Jun 12 2021