A174440 Partial sums of A022544.

3, 9, 16, 27, 39, 53, 68, 87, 108, 130, 153, 177, 204, 232, 262, 293, 326, 361, 399, 438, 480, 523, 567, 613, 660, 708, 759, 813, 868, 924, 981, 1040, 1100, 1162, 1225, 1291, 1358, 1427, 1497, 1568, 1643, 1719, 1796, 1874, 1953, 2036, 2120, 2206, 2293, 2381

Offset

1,1

Comments

Partial sums of numbers that are not the sum of 2 squares. The subsequence of primes in this partial sum begins: 3, 53, 293, 523, 613, 1291, 1427, 2293, 2381, 2657, 3041, 4013, 5779, 6337, 7687, 9337, 9511, 10039. The subsequence of squares in this partial sum begins: 9, 16, 361, 1225.

Links

Table of n, a(n) for n=1..50.

Formula

a(n) = SUM[i=1..n] A022544(i) = SUM[i=1..n] {numbers that are not the sum of 2 squares} = SUM[i=1..n] {numbers having some prime factor p == 3 (mod 4) to an odd power}.

Example

a(22) = 3 + 6 + 7 + 11 + 12 + 14 + 15 + 19 + 21 + 22 + 23 + 24 + 27 + 28 + 30 + 31 + 33 + 35 + 38 + 39 + 42 + 43 = 523 is prime.

Crossrefs

Cf. A001481, A022544.

Sequence in context: A024385 A212566 A061942 * A244475 A212870 A306447

Adjacent sequences: A174437 A174438 A174439 * A174441 A174442 A174443

Keyword

nonn

Author

Jonathan Vos Post, Mar 20 2010

Status

approved