A173509 Partial sums of A038568.

1, 2, 4, 5, 8, 10, 13, 14, 18, 21, 25, 26, 31, 33, 38, 41, 46, 50, 55, 56, 62, 67, 73, 74, 81, 83, 90, 93, 100, 104, 111, 116, 123, 129, 136, 137, 145, 148, 156, 161, 169, 176, 184, 185, 194, 196, 205, 209, 218, 223, 232, 239, 248, 256, 265, 266, 276, 279, 289, 296

Offset: 0

Author

Jonathan Vos Post, Feb 20 2010

Keywords

• easy
• nonn

Comments

Partial sums of numerators in canonical bijection from positive integers to positive rationals. The companion sequence for denominators is A173467, summing A038569. The subsequence of squares in this partial sum begins: 1, 4, 25, 81, 100, 137, 169, 196, 256, 289, 576. The subsequence of primes in this partial sum begins: 2, 5, 13, x, 41, 67, 73, 83, 223, 239, 337, 353, 379, 401, 419, 449, 479, 491, 503, 563.

Examples

			a(93) = 1 + 1 + 2 + 1 + 3 + 2 + 3 + 1 + 4 + 3 + 4 + 1 + 5 + 2 + 5 + 3 + 5 + 4 + 5 + 1 + 6 + 5 + 6 + 1 + 7 + 2 + 7 + 3 + 7 + 4 + 7 + 5 + 7 + 6 + 7 + 1 + 8 + 3 + 8 + 5 + 8 + 7 + 8 + 1 + 9 + 2 + 9 + 4 + 9 + 5 + 9 + 7 + 9 + 8 + 9 + 1 + 10 + 3 + 10 + 7 + 10 + 9 + 10 + 1 + 11 + 2 + 11 + 3 + 11 + 4 + 11 + 5 + 11 + 6 + 11 + 7 + 11 + 8 + 11 + 9 + 11 + 10 + 11 + 1 + 12 + 5 + 12 + 7 + 12 + 11 + 12 + 1 + 13 + 2.
		

Crossrefs

Cf. A038568, A038569, A173467.

Formula

a(n) = SUM[i=0..n] A038568(i).