A320688 - OEIS

%I #14 Dec 19 2024 23:40:08

%S 3,4,6,11,10,24,26,34,26,33,50,67,72,46,70,109,96,132,122,153,132,145,

%T 174,229,208,175,194,287,232,244,338,267,276,345,374,239,392,396,424,

%U 390,484,373,514,563,618,424,654,821,442,557,890,814,668,741,580,642,990,811,982,968,772

%N Sum of the square excess A056892 of the primes between two squares.

%C Consider the primes p1,...,pK between two squares n^2 and (n+1)^2, and take the sum of the differences: (p1 - n^2) + ... + (pK - n^2). Obviously this equals (sum of these primes) - (number of these primes) * n^2.

%H Robert Israel, <a href="/A320688/b320688.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A108314(n) - A014085(n)*A000290(n), where A000290(n) = n^2.

%p R:= NULL: p:= 2: n:= 1: t:= 0:

%p while n <= 100 do

%p     t:= t + p-n^2;

%p     p:= nextprime(p);

%p     if p > (n+1)^2 then

%p      R:= R, t; t:= 0; n:= n+1;

%p     fi:

%p od:

%p R; # _Robert Israel_, Dec 17 2024

%o (PARI) a(n,s=0)={forprime(p=n^2,(n+1)^2,s+=p-n^2);s}

%Y Cf. A014085, A000290, A108314, A106044.

%Y Row sums of A056892, read as a table.

%K nonn

%O 1,1

%A _M. F. Hasler_, Oct 19 2018