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A305736
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Number of integer partitions of n whose greatest common divisor is composite (nonprime and > 1).
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1
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0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 4, 0, 1, 1, 5, 0, 4, 0, 8, 1, 1, 0, 14, 1, 1, 3, 16, 0, 10, 0, 22, 1, 1, 1, 41, 0, 1, 1, 45, 0, 18, 0, 57, 9, 1, 0, 94, 1, 8, 1, 102, 0, 38, 1, 138, 1, 1, 0, 221, 0, 1, 17, 231, 1, 59, 0, 298, 1, 22
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OFFSET
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1,8
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LINKS
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FORMULA
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EXAMPLE
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The a(12) = 4 integer partitions are (12), (8 4), (6 6), (4 4 4).
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], !(GCD@@#==1||PrimeQ[GCD@@#])&]], {n, 0, 20}]
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PROG
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(PARI) seq(n)={dirmul(vector(n, n, numbpart(n)), dirmul(vector(n, n, moebius(n)), vector(n, n, n>1&&!isprime(n))))} \\ Andrew Howroyd, Jun 22 2018
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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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