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A046641
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a(n) is the smallest positive integer m such that the number of partitions p(m) = A000041(m) is divisible by n.
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10
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1, 2, 3, 11, 4, 9, 5, 11, 14, 9, 6, 21, 28, 10, 7, 15, 54, 21, 20, 58, 10, 8, 32, 21, 24, 28, 14, 11, 26, 9, 44, 66, 16, 94, 18, 21, 86, 47, 129, 66, 35, 10, 27, 15, 14, 75, 56, 70, 19, 74, 178, 62, 52, 340, 18, 11, 20, 26, 54, 124, 115, 101, 24, 66, 84, 21, 47, 94, 32, 19
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OFFSET
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1,2
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COMMENTS
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The initial term could also be taken to be 0.
From the formula a(p(n)) = n, it follows that every positive integer appears in this sequence. - Franklin T. Adams-Watters, Feb 09 2016
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LINKS
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FORMULA
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EXAMPLE
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The first partition number divisible by 9 is p(14) = 135, so a(9) = 14.
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MATHEMATICA
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Table[SelectFirst[Range[10^3], Divisible[PartitionsP@ #, n] &], {n, 70}] (* Michael De Vlieger, Feb 10 2016, Version 10 *)
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PROG
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(PARI) a(n) = my(m = 1); while(numbpart(m) % n, m++); m; \\ Michel Marcus, Feb 10 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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