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a(n) = (sum of first n primes) * n.
2

%I #17 May 10 2019 21:50:52

%S 2,10,30,68,140,246,406,616,900,1290,1760,2364,3094,3934,4920,6096,

%T 7480,9018,10792,12780,14952,17402,20102,23112,26500,30186,34128,

%U 38388,42920,47790,53320,59232,65604,72318,79660,87372,95608,104386,113646,123480

%N a(n) = (sum of first n primes) * n.

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

%H T. D. Noe, <a href="/A167214/b167214.txt">Table of n, a(n) for n = 1..1000</a>

%H Asymptotic Expression for a(n) is a direct extension of asymptotic expression for <a href="http://oeis.org/A007504">A007504</a>(n).

%F a(n) = n*A007504(n). - _R. J. Mathar_, Oct 31 2009

%p 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

%p seq(n*add(ithprime(j), j = 1 .. n), n = 1 .. 40); # _Emeric Deutsch_, Nov 01 2009

%t s=0; Table[s=s+Prime[n]; s*n, {n, 50}]

%K nonn,easy

%O 1,1

%A _Pratik Poddar_, Oct 30 2009

%E More terms from _R. J. Mathar_ and _Emeric Deutsch_, Oct 31 2009