A062020 a(n) = Sum_{i=1..n} Sum_{j=1..i} (prime(i) - prime(j)).

0, 1, 6, 17, 44, 81, 142, 217, 324, 485, 666, 913, 1208, 1529, 1906, 2373, 2936, 3533, 4238, 5019, 5840, 6787, 7822, 8995, 10360, 11825, 13342, 14967, 16648, 18445, 20662, 23003, 25536, 28135, 31074, 34083, 37308, 40755, 44354, 48187, 52260

Offset

1,3

Links

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

Formula

a(n) = a(n-1) + n*prime(n) - Sum_{i = 1..n} prime(i), with a(0) = 0.

a(n) = 2*a(n-1) - a(n-2) + (n-1)*(prime(n) - prime(n-1)), with a(1) = 0, a(2) = 1.

a(n) = Sum_{j=1..n} (2*j - (n+1))*prime(j) = 2*A014285(n) - (n+1)*A007504(n). - G. C. Greubel, May 04 2022

Example

a(3) = (5-2) + (5-3) + (3-2) = 6.

Mathematica

a[n_]:= a[n]= If[n<3, (n-1), 2*a[n-1] -a[n-2] +(n-1)*(Prime[n] -Prime[n-1])];
Table[a[n], {n, 50}] (* G. C. Greubel, May 04 2022 *)

Prog

(SageMath)
@CachedFunction
def a(n): # A062020
    if (n<3): return (n-1)
    else: return 2*a(n-1) - a(n-2) + (n-1)*(nth_prime(n) - nth_prime(n-1))
[a(n) for n in (1..50)] # G. C. Greubel, May 04 2022

Crossrefs

Cf. A000040, A007504, A014285, A062021, A062022.

Sequence in context: A171507 A099858 A232567 * A066183 A262297 A048746

Adjacent sequences: A062017 A062018 A062019 * A062021 A062022 A062023

Keyword

nonn

Author

Amarnath Murthy, Jun 02 2001

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 05 2001

Name edited by G. C. Greubel, May 04 2022

Status

approved