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A305736
Number of integer partitions of n whose greatest common divisor is composite (nonprime and > 1).
1
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
OFFSET
1,8
LINKS
FORMULA
a(n) = A018783(n) - A305735(n). - 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)={dirmul(vector(n, n, numbpart(n)), dirmul(vector(n, n, moebius(n)), vector(n, n, n>1&&!isprime(n))))} \\ Andrew Howroyd, Jun 22 2018
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 22 2018
STATUS
approved