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

0,2

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.

Links

Table of n, a(n) for n=0..59.

Formula

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

Example

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.

Sequence in context: A365315 A179509 A157007 * A007729 A174868 A268381

Adjacent sequences: A173506 A173507 A173508 * A173510 A173511 A173512

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 20 2010

Status

approved