A202297 - OEIS

%I #29 Jan 16 2024 11:37:02

%S 0,34,1700,38100,403860,2572620,11863176,43468984,134426588,364794428,

%T 890218104,1998186072,4178379984,8232956688,15425693558,27713583130,

%U 47890427740,80095432340,130221623840,206201325600,318555575550,481995772662,715882366878,1043383039482

%N Product of the sum of the first n^2 primes by the sum of the first (n+1)^2 primes.

%H Vincenzo Librandi, <a href="/A202297/b202297.txt">Table of n, a(n) for n = 0..200</a>

%H Stephen Balaban, <a href="/A202297/a202297.txt">Clojure Code for generating the sequence</a> usage: clj primes.txt n where n is the number of elements of this sequence to print

%F a(n) = A109724(n)*A109724(n+1).

%t Table[(Plus@@Prime[Range[n^2]]) (Plus@@Prime[Range[(n + 1)^2]]), {n, 0, 19}] (* _Alonso del Arte_, Dec 16 2011 *)

%o (Clojure) (defn prod-prime-matrix [n] (* (sum-matrix (first-n2-primes n)) (sum-matrix (first-n2-primes (inc n)))))

%o (Magma) A109724:=func<n|&+[NthPrime(h): h in [1..n^2]]>; [0] cat [A109724(n)*A109724(n+1): n in [1..23]];  // _Bruno Berselli_, Dec 16 2011

%o (PARI) a(n) = vecsum(primes(n^2))* vecsum(primes((n+1)^2)); \\ _Michel Marcus_, Mar 20 2023

%Y Cf. A109724.

%K nonn

%O 0,2

%A _Stephen Balaban_, Dec 15 2011

%E More terms from _Bruno Berselli_, Dec 16 2011