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A342604 a(n) = Sum_{j=1..n} A003718(j-1)*prime(j).

%I A342604 #11 Mar 17 2021 13:25:28
%S A342604 2,5,10,17,39,52,69,126,195,224,255,403,649,821,868,921,1216,1826,
%T A342604 2496,2851,2924,3003,3501,4836,6776,8291,8909,9016,9125,9916,12583,
%U A342604 17168,21963,24882,25925,26076,26233,27537,32213,41901,54431,64567,69915,71459,71656,71855,73754,81782,100850,129704
%N A342604 a(n) = Sum_{j=1..n} A003718(j-1)*prime(j).
%H A342604 Robert Israel, <a href="/A342604/b342604.txt">Table of n, a(n) for n = 1..10000</a>
%e A342604 a(3) = A003718(0)*prime(1) + A003718(1)*prime(2) + A003718(2)*prime(3) = 1*2 + 1*3 + 1*5 = 10.
%p A342604 p:= 1: R:= NULL:
%p A342604 for n from 0 to 14 do
%p A342604   for k from 0 to n do
%p A342604     p:= nextprime(p);
%p A342604     R:= R, binomial(n,k)*p
%p A342604 od od:
%p A342604 ListTools:-PartialSums([R]):
%Y A342604 Cf. A003718, A342605, A342606.
%K A342604 nonn
%O A342604 1,1
%A A342604 _J. M. Bergot_ and _Robert Israel_, Mar 16 2021