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A201025
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Number of partitions of n such that the number of parts and the smallest part are not coprime.
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3
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0, 0, 0, 1, 1, 1, 1, 3, 4, 5, 7, 10, 12, 15, 18, 25, 30, 39, 47, 62, 74, 94, 113, 144, 173, 215, 261, 324, 390, 476, 571, 697, 832, 1004, 1196, 1439, 1706, 2038, 2409, 2868, 3380, 4001, 4702, 5550, 6504, 7645, 8938, 10478, 12218, 14277, 16612, 19363, 22481
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listen;
history;
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internal format)
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OFFSET
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1,8
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..400
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FORMULA
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a(n) = A000041(n) - A200928(n).
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EXAMPLE
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a(7) = 1: [2,5];
a(8) = 3: [2,2,2,2], [4,4], [2,6];
a(9) = 4: [2,2,2,3], [3,3,3], [4,5], [2,7];
a(10) = 5: [2,2,3,3], [2,2,2,4], [3,3,4], [4,6], [2,8];
a(11) = 7: [2,3,3,3], [2,2,3,4], [3,4,4], [2,2,2,5], [3,3,5], [4,7], [2,9].
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MAPLE
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b:= proc(n, j, t, s) option remember;
add (b(n-i, i, irem(t+1, s), s), i=j..iquo(n, 2))+
`if`(igcd(t, s)>1, 1, 0)
end:
a:= n-> add (b(n-i, i, 2, i), i=2..iquo(n, 2)):
seq (a(n), n=1..60);
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CROSSREFS
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Cf. A000041, A199889, A200928.
Sequence in context: A048342 A159560 A030502 * A073957 A162311 A003312
Adjacent sequences: A201022 A201023 A201024 * A201026 A201027 A201028
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Nov 25 2011
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STATUS
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approved
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