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A139562 Sum of primes < n^2. 2
0, 0, 5, 17, 41, 100, 160, 328, 501, 791, 1060, 1593, 2127, 2914, 3831, 4661, 6801, 7982, 9523, 11599, 13887, 16840, 20059, 23592, 26940, 32353, 37561, 42468, 48494, 55837, 62797, 70241, 80189, 89672, 100838, 111587, 124211, 136114, 148827 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

SumP(n) ~ Pi(n^2). A heuristic derivation of this is found in the second link.

For large n, a(n) is closely approximated by Pi(n^4). Eg., for n = 55, SumP(55^2) = 605877 and Pi(55^4) = 611827 with error = .0098..

For n = 10^5, SumP (10) = 2220822432581729238 and Pi(10^20) = 2220819602560918840 with error = 0.0000012...

LINKS

Table of n, a(n) for n=0..38.

Cino Hilliard SumprimesGmp program.

Cino Hilliard Sum of Primes less than n".

FORMULA

Pi(x) is the prime counting function or the number of primes <= x. SunP(n) = sum of primes <= n.

EXAMPLE

For n = 3, n^2=9, sum of primes <= 9 = 2+3+5+7 = 17, the 4th entry in the sequence.

PROG

Sumprimesgmp.c in first link.

CROSSREFS

Cf. A046731, A000720, A006880.

Sequence in context: A106972 A086499 A097123 * A201599 A246636 A146794

Adjacent sequences:  A139559 A139560 A139561 * A139563 A139564 A139565

KEYWORD

nonn

AUTHOR

Cino Hilliard, Jun 11 2008

STATUS

approved

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Last modified February 26 18:29 EST 2020. Contains 332293 sequences. (Running on oeis4.)