A167214 a(n) = (sum of first n primes) * n.

2, 10, 30, 68, 140, 246, 406, 616, 900, 1290, 1760, 2364, 3094, 3934, 4920, 6096, 7480, 9018, 10792, 12780, 14952, 17402, 20102, 23112, 26500, 30186, 34128, 38388, 42920, 47790, 53320, 59232, 65604, 72318, 79660, 87372, 95608, 104386, 113646, 123480

Offset: 1

Author

Pratik Poddar, Oct 30 2009

Keywords

• nonn
• easy

Comments

a(n) has the asymptotic expression a(n) ~ n^3 * log(n) / 2.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Asymptotic Expression for a(n) is a direct extension of asymptotic expression for A007504(n).

Programs

Maple

A007504 := proc(n) add(ithprime(i), i=1..n) ; end: A167214 := proc(n) n*A007504(n) ; end: seq(A167214(n), n=1..80) ; # R. J. Mathar, Oct 31 2009
seq(n*add(ithprime(j), j = 1 .. n), n = 1 .. 40); # Emeric Deutsch, Nov 01 2009

Mathematica

s=0; Table[s=s+Prime[n]; s*n, {n, 50}]
Module[{nn=50,spr},spr=Accumulate[Prime[Range[nn]]];Times@@@Thread[{Range[nn],spr}]] (* Harvey P. Dale, Jul 23 2025 *)

Formula

a(n) = n*A007504(n). - R. J. Mathar, Oct 31 2009

Extensions

More terms from R. J. Mathar and Emeric Deutsch, Oct 31 2009