A161569 Sum of first n nonprimes minus their indices.

0, 2, 5, 9, 13, 17, 22, 28, 34, 40, 47, 55, 63, 71, 80, 89, 98, 107, 116, 126, 137, 148, 159, 170, 181, 193, 205, 217, 230, 244, 258, 272, 287, 302, 317, 332, 347, 363, 379, 395, 411, 427, 444, 462, 480, 498, 516, 534, 553, 572, 591, 611, 632, 653, 674, 695, 716

Offset

1,2

Comments

The sum of first n nonprimes is in A051349.

Partial sums of A073425. - Jaroslav Krizek, Jun 27 2009

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = A051349(n)-n*(n+1)/2.

a(n) = a(n-1)+A018252(n)-n, a(1) = 0. - Klaus Brockhaus, Dec 16 2010

Example

a(1) = 1-1 = 0; a(2) = 0+4-2 = 2, a(3) = 2+6-3 = 5; a(4) = 5+8-4 = 9.

Mathematica

Accumulate[With[{nps=Select[Range[100], !PrimeQ[#]&]}, #[[1]]-#[[2]]&/@Thread[{nps, Range[Length[nps]]}]]] (* Harvey P. Dale, Apr 29 2026 *)

Crossrefs

Cf. A073425, A051349, A018252, A112997.

Sequence in context: A050877 A063203 A130244 * A263086 A353036 A182814

Adjacent sequences: A161566 A161567 A161568 * A161570 A161571 A161572

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, Jun 14 2009

Extensions

a(54)-a(57) from Stefano Spezia, May 26 2025

Status

approved