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A320688 Sum of the square excess A056892 of the primes between two squares. 1
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 (list; graph; refs; listen; history; text; internal format)
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
FORMULA
a(n) = A108314(n) - A014085(n)*A000290(n), where A000290(n) = n^2.
PROG
(PARI) a(n, s=0)={forprime(p=n^2, (n+1)^2, s+=p-n^2); s}
CROSSREFS
Row sums of A056892, read as a table.
Equals A108314 - A014085 * A000290.
Sequence in context: A091424 A092839 A185874 * A352734 A275418 A047413
KEYWORD
nonn
AUTHOR
M. F. Hasler, Oct 19 2018
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)