A316322 Sum of piles of first n primes: a(n) = Sum(prime(i)*(2*i-1): 1<=i<=n).

2, 11, 36, 85, 184, 327, 548, 833, 1224, 1775, 2426, 3277, 4302, 5463, 6826, 8469, 10416, 12551, 15030, 17799, 20792, 24189, 27924, 32107, 36860, 42011, 47470, 53355, 59568, 66235, 73982, 82235, 91140, 100453, 110734, 121455, 132916, 145141, 158000, 171667, 186166, 201189, 217424, 234215, 251748

Offset: 1

Author

N. J. A. Sloane, Jul 03 2018, based on Reinhard Zumkeller's A083215

Keywords

• nonn

Examples

			............................................ 7
........................... 5 ............ 7 5 7
............ 3 .......... 5 3 5 ........ 7 5 3 5 7
2 ........ 3 2 3 ...... 5 3 2 3 5 .... 7 5 3 2 3 5 7
a(1)=2 ... a(2)=11 .... a(3)=36 ...... a(4)=85.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A083215, A014285, A007504, A167214, A023662, A062020.

Programs

Maple

seq(add((2*i-1)*ithprime(i),i=1..n), n=1..80); # Ridouane Oudra, Feb 19 2025

Mathematica

nxt[{n_, a_}] := {n + 1, a + Prime[n + 1] (2 n + 1)}; NestList[nxt,{1,2},50][[All,2]] (* Harvey P. Dale, Jul 05 2018 *)

PARI

a(n) = sum(i=1, n, prime(i)*(2*i-1)); \\ Michel Marcus, Jan 22 2022

Formula

From Ridouane Oudra, Feb 19 2025: (Start)

a(n) = Sum_{i=1..n} Sum_{j=1..n} max(prime(i), prime(j)).

a(n) = 2*A014285(n) - A007504(n).

a(n) = 2*A167214(n) - A023662(n).

a(n) = A167214(n) + A062020(n). (End)