A320688 Sum of the square excess A056892 of the primes between two squares.

3, 4, 6, 11, 10, 24, 26, 34, 26, 33, 50, 67, 72, 46, 70, 109, 96, 132, 122, 153, 132, 145, 174, 229, 208, 175, 194, 287, 232, 244, 338, 267, 276, 345, 374, 239, 392, 396, 424, 390, 484, 373, 514, 563, 618, 424, 654, 821, 442, 557, 890, 814, 668, 741, 580, 642, 990, 811, 982, 968, 772

Offset

1,1

Comments

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.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

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

Maple

R:= NULL: p:= 2: n:= 1: t:= 0:
while n <= 100 do
    t:= t + p-n^2;
    p:= nextprime(p);
    if p > (n+1)^2 then
     R:= R, t; t:= 0; n:= n+1;
    fi:
od:
R; # Robert Israel, Dec 17 2024

Prog

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

Crossrefs

Cf. A014085, A000290, A108314, A106044.

Row sums of A056892, read as a table.

Sequence in context: A091424 A092839 A185874 * A352734 A275418 A047413

Adjacent sequences: A320685 A320686 A320687 * A320689 A320690 A320691

Keyword

nonn

Author

M. F. Hasler, Oct 19 2018

Status

approved