A014285 a(n) = Sum_{j=1..n} j*prime(j).

2, 8, 23, 51, 106, 184, 303, 455, 662, 952, 1293, 1737, 2270, 2872, 3577, 4425, 5428, 6526, 7799, 9219, 10752, 12490, 14399, 16535, 18960, 21586, 24367, 27363, 30524, 33914, 37851, 42043, 46564, 51290, 56505, 61941, 67750, 73944, 80457, 87377, 94716, 102318

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Two consecutive terms cannot both be divisible by 4. - Tamas Sandor Nagy, Aug 04 2024

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Partial sums of A033286. - Michel Marcus, Jun 18 2019

Cf. A007504, A014148.

Programs

Magma

[&+[k*NthPrime(k): k in [1..n]]: n in [1..40]];  // Bruno Berselli, Apr 30 2011

Mathematica

Join[{s=2},Table[s+=Prime[n]*n,{n,2,33}]] (* Vladimir Joseph Stephan Orlovsky, Dec 30 2010 *)
Accumulate[Table[i*Prime[i],{i,40}]] (* Harvey P. Dale, Sep 10 2014 *)

PARI

{a(n) = sum(j=1,n, j*prime(j))}; \\ G. C. Greubel, Jun 18 2019

Sage

[sum(j*nth_prime(j) for j in (1..n)) for n in (1..40)] # G. C. Greubel, Jun 18 2019

Formula

a(n) = n*A007504(n) - Sum_{k=1..n-1} A007504(k) = n*A007504(n) - A014148(n-1). - Pontus von Brömssen, Aug 29 2021

Extensions

Offset changed to 1 and six terms added by Bruno Berselli, Apr 30 2011