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

%I A316322 #19 Jul 09 2025 04:47:42
%S A316322 2,11,36,85,184,327,548,833,1224,1775,2426,3277,4302,5463,6826,8469,
%T A316322 10416,12551,15030,17799,20792,24189,27924,32107,36860,42011,47470,
%U A316322 53355,59568,66235,73982,82235,91140,100453,110734,121455,132916,145141,158000,171667,186166,201189,217424,234215,251748
%N A316322 Sum of piles of first n primes: a(n) = Sum(prime(i)*(2*i-1): 1<=i<=n).
%H A316322 Seiichi Manyama, <a href="/A316322/b316322.txt">Table of n, a(n) for n = 1..10000</a>
%F A316322 From _Ridouane Oudra_, Feb 19 2025: (Start)
%F A316322 a(n) = Sum_{i=1..n} Sum_{j=1..n} max(prime(i), prime(j)).
%F A316322 a(n) = 2*A014285(n) - A007504(n).
%F A316322 a(n) = 2*A167214(n) - A023662(n).
%F A316322 a(n) = A167214(n) + A062020(n). (End)
%e A316322 ............................................ 7
%e A316322 ........................... 5 ............ 7 5 7
%e A316322 ............ 3 .......... 5 3 5 ........ 7 5 3 5 7
%e A316322 2 ........ 3 2 3 ...... 5 3 2 3 5 .... 7 5 3 2 3 5 7
%e A316322 a(1)=2 ... a(2)=11 .... a(3)=36 ...... a(4)=85.
%p A316322 seq(add((2*i-1)*ithprime(i),i=1..n), n=1..80); # _Ridouane Oudra_, Feb 19 2025
%t A316322 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 *)
%o A316322 (PARI) a(n) = sum(i=1, n, prime(i)*(2*i-1)); \\ _Michel Marcus_, Jan 22 2022
%Y A316322 Cf. A083215, A014285, A007504, A167214, A023662, A062020.
%K A316322 nonn
%O A316322 1,1
%A A316322 _N. J. A. Sloane_, Jul 03 2018, based on _Reinhard Zumkeller_'s A083215