proposed

approved

editing

proposed

a(n) = A056892A108314(n) - A014085(n)*A000290(n), where A000290(n) = n^2.

Equals A056892 A108314 - A014085 * A000290.

Sum of differences the square excess A056892 of the primes between two squares and the smaller square.

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.

Sum of differences of the larger square and primes between two squares and the smaller square.

a(n) = A056892(n) - A014085(n)*A000290(n), where A000290(n) = n^2.

Row sums of A056892, read as a table.

Equals A056892 - A014085 * A000290.

allocated for M. F. Hasler

Sum of differences of the larger square and 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

1,1

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).

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

Cf. A014085, A000290, A108314, A106044.

allocated

nonn,changed

M. F. Hasler, Oct 19 2018

approved

editing

allocated for M. F. Hasler

allocated

approved