A079725 Sum of composite numbers less than n-th prime.

0, 0, 4, 10, 37, 49, 94, 112, 175, 305, 335, 505, 622, 664, 799, 1049, 1329, 1389, 1709, 1916, 1988, 2368, 2611, 3041, 3692, 3989, 4091, 4406, 4514, 4847, 6407, 6794, 7464, 7602, 8898, 9048, 9818, 10618, 11113, 11963, 12843, 13023, 14697, 14889, 15474

Offset

1,3

Links

Table of n, a(n) for n=1..45.

Formula

a(n) = prime(n)*(prime(n)+1)/2 - sum_{1..n} prime(k) - 1.

Asymptotic expression: a(n) ~ n^2 * log(n)^2 / 2.

Example

Prime(6) = 13, so a(6) = 4 + 6 + 8 + 9 + 1 0 + 12 = 49 = 13*14/2 - 13 - 11 - 7 - 5 - 3 - 2 - 1.

Maple

with(numtheory): A079725 := proc(n) local i:
RETURN(ithprime(n)*(ithprime(n)+1)/2 add(ithprime(i), i=1..n)-1):
end;

Mathematica

a[n_] := Block[{p = Prime[n], k}, k = p(p + 1)/2 - 1 - Sum[Prime[i], {i, 1, n}]]; Table[ a[n], {n, 1, 45}]

Crossrefs

Equals A000217(Prime_n) - A007504(n) - 1 = A034953 - A007504 - A000012.

Partial sums of A054265.

Sequence in context: A345245 A197552 A052572 * A154152 A357051 A370781

Adjacent sequences: A079722 A079723 A079724 * A079726 A079727 A079728

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 18 2003

Extensions

Edited and extended by Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Robert G. Wilson v and T. D. Noe, Feb 18 2003

Status

approved