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 A305736 Number of integer partitions of n whose greatest common divisor is composite (nonprime and > 1). 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 LINKS FORMULA a(n) = A018783(n) - A305735(n) for n > 0. - Andrew Howroyd, Jun 22 2018 EXAMPLE The a(12) = 4 integer partitions are (12), (8 4), (6 6), (4 4 4). MATHEMATICA Table[Length[Select[IntegerPartitions[n], !(GCD@@#==1||PrimeQ[GCD@@#])&]], {n, 0, 20}] PROG (PARI) seq(n)={concat([1], dirmul(vector(n, n, numbpart(n)), dirmul(vector(n, n, moebius(n)), vector(n, n, n>1&&!isprime(n)))))} \\ Andrew Howroyd, Jun 22 2018 CROSSREFS Cf. A000040, A000837, A018783, A100953, A289508, A302698, A305563, A305731, A305735. Sequence in context: A318758 A124790 A325734 * A324642 A326757 A147787 Adjacent sequences:  A305733 A305734 A305735 * A305737 A305738 A305739 KEYWORD nonn AUTHOR Gus Wiseman, Jun 22 2018 STATUS approved

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Last modified February 25 11:39 EST 2020. Contains 332233 sequences. (Running on oeis4.)