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

Author

Jonathan Vos Post, Mar 20 2010

Keywords

• nonn

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.

Examples

			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.

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}.