A023862 a(n) = 1*t(n) + 2*t(n-1) + ... + k*t(n+1-k), where k=floor((n+1)/2) and t = A008578 ({1} U primes).

1, 2, 7, 11, 26, 40, 76, 104, 171, 219, 331, 397, 566, 672, 912, 1046, 1369, 1561, 1985, 2223, 2762, 3026, 3688, 4030, 4833, 5215, 6179, 6631, 7764, 8318, 9630, 10270, 11793, 12499, 14245, 15019, 17006, 17930, 20176, 21182, 23701, 24837, 27645, 28965, 32084, 33504

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

CF. A000040, A008578.

Programs

Magma

[1] cat [(&+[j*NthPrime(n-j): j in [1..Floor((n+1)/2)]]): n in [2..50]]; // G. C. Greubel, Jun 12 2019

Mathematica

Join[{1}, Table[Sum[j*Prime[n-j], {j,1,Floor[(n+1)/2]}], {n, 2, 50}]] (* G. C. Greubel, Jun 12 2019 *)

PARI

a(n) = sum(j=1, floor((n+1)/2), j*prime(n-j));
vector(50, n, if(n==1, 1, a(n))) \\ G. C. Greubel, Jun 12 2019

Sage

[1]+[sum(j*nth_prime(n-j) for j in (1..floor((n+1)/2))) for n in (2..50)] # G. C. Greubel, Jun 12 2019

Extensions

Title simplified by Sean A. Irvine, Jun 12 2019