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A285902
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Total number of partitions of all positive integers <= n into an even number of consecutive parts.
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4
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0, 0, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 14, 15, 16, 16, 17, 18, 20, 20, 21, 22, 23, 23, 25, 26, 27, 28, 29, 30, 32, 32, 33, 34, 35, 36, 38, 39, 40, 40, 41, 42, 44, 45, 46, 47, 49, 49, 51, 52, 53, 54, 55, 56, 58, 58, 60, 61, 62, 63, 65, 66, 67, 67, 68, 69, 72, 73, 74, 76, 77, 77, 79, 80, 81, 82
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OFFSET
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1,5
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COMMENTS
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a(n) is also the total number of odd divisors of k greater than sqrt(2*k), for k = 1..n.
Conjecture: a(n) is also the total number of pairs of equidistant subparts of all symmetric representations of sigma of all positive integers <= n.
For more information about the "subparts" of the symmetric representation of sigma see A279387 and A237593.
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LINKS
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FORMULA
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CROSSREFS
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Cf. A001227, A060831, A082647, A196020, A235791, A236104, A237048, A237270, A237591, A237593, A237270, A279387, A245092, A262626, A285901.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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