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A173509
Partial sums of A038568.
0
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.
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
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 20 2010
STATUS
approved