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A200727
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Number of partitions of n such that the number of parts is not divisible by the greatest part.
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5
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0, 1, 1, 3, 4, 8, 9, 16, 22, 33, 42, 61, 79, 110, 143, 192, 246, 325, 411, 535, 676, 865, 1081, 1371, 1704, 2136, 2642, 3283, 4035, 4979, 6082, 7453, 9067, 11043, 13365, 16197, 19516, 23531, 28239, 33894, 40513, 48425, 57667, 68661, 81497, 96679, 114370
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OFFSET
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1,4
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COMMENTS
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Also number of partitions of n such that the greatest part is not divisible by the number of parts. Equivalence can be shown using Ferrers-Young diagrams.
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LINKS
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EXAMPLE
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The number of parts is not divisible by the greatest part:
a(5) = 4: [1,2,2], [2,3], [1,4], [5];
a(6) = 8: [1,1,1,1,2], [2,2,2], [1,1,1,3], [3,3], [1,1,4], [2,4], [1,5], [6].
The greatest part is not divisible by the number of parts:
a(5) = 4: [1,1,1,1,1], [1,1,1,2], [1,2,2], [2,3];
a(6) = 8: [1,1,1,1,1,1], [1,1,1,1,2], [1,1,2,2], [2,2,2], [1,1,1,3], [3,3], [1,1,4], [1,5].
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MAPLE
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b:= proc(n, j, t) option remember;
add(b(n-i, i, t+1), i=j..iquo(n, 2))+
`if`(irem(t, n)>0, 1, 0)
end:
a:= n-> b(n, 1, 1):
seq(a(n), n=1..50);
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MATHEMATICA
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b[n_, j_, t_] := b[n, j, t] = Sum[b[n-i, i, t+1], {i, j, Quotient[n, 2]}] + If[Mod[t, n]>0, 1, 0]; a[n_] := b[n, 1, 1]; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Feb 05 2017, translated from Maple *)
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CROSSREFS
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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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