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A305735
Number of integer partitions of n whose greatest common divisor is a prime number.
3
0, 1, 1, 1, 1, 3, 1, 3, 2, 7, 1, 10, 1, 15, 8, 17, 1, 34, 1, 37, 16, 56, 1, 80, 6, 101, 27, 122, 1, 208, 1, 209, 57, 297, 20, 410, 1, 490, 102, 599, 1, 901, 1, 948, 194, 1255, 1, 1690, 14, 1985, 298, 2337, 1, 3327, 61, 3597, 491, 4565, 1, 6031, 1, 6842, 802
OFFSET
1,6
LINKS
FORMULA
a(n) = Sum_{d|n} A143519(d) * A000041(n/d). - Andrew Howroyd, Jun 22 2018
EXAMPLE
The a(10) = 7 integer partitions are (82), (64), (622), (55), (442), (4222), (22222).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], PrimeQ[GCD@@#]&]], {n, 20}]
PROG
(PARI) seq(n)={dirmul(vector(n, n, numbpart(n)), dirmul(vector(n, n, moebius(n)), vector(n, n, isprime(n))))} \\ Andrew Howroyd, Jun 22 2018
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 22 2018
STATUS
approved