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

2, 5, 10, 17, 39, 52, 69, 126, 195, 224, 255, 403, 649, 821, 868, 921, 1216, 1826, 2496, 2851, 2924, 3003, 3501, 4836, 6776, 8291, 8909, 9016, 9125, 9916, 12583, 17168, 21963, 24882, 25925, 26076, 26233, 27537, 32213, 41901, 54431, 64567, 69915, 71459, 71656, 71855, 73754, 81782, 100850, 129704

Offset: 1

Author

J. M. Bergot and Robert Israel, Mar 16 2021

Keywords

• nonn

Examples

			a(3) = A003718(0)*prime(1) + A003718(1)*prime(2) + A003718(2)*prime(3) = 1*2 + 1*3 + 1*5 = 10.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003718, A342605, A342606.

Programs

Maple

p:= 1: R:= NULL:
for n from 0 to 14 do
  for k from 0 to n do
    p:= nextprime(p);
    R:= R, binomial(n,k)*p
od od:
ListTools:-PartialSums([R]):