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A305735 Number of integer partitions of n whose greatest common divisor is a prime number. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..63.

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

CROSSREFS

Cf. A000040, A000041, A000837, A018783, A100953, A143519, A289508, A302698, A305563, A305731.

Sequence in context: A085671 A126324 A035557 * A248947 A133916 A058589

Adjacent sequences:  A305732 A305733 A305734 * A305736 A305737 A305738

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 22 2018

STATUS

approved

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Last modified May 16 12:30 EDT 2021. Contains 343947 sequences. (Running on oeis4.)