A316432 Number of integer partitions of n whose length is equal to the GCD of all parts.

1, 0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 2, 0, 3, 2, 3, 0, 5, 0, 3, 4, 5, 0, 8, 1, 6, 6, 6, 0, 11, 0, 8, 10, 8, 2, 18, 0, 9, 14, 15, 0, 19, 0, 16, 21, 11, 0, 34, 1, 16, 24, 24, 0, 30, 10, 27, 30, 14, 0, 71, 0, 15, 34, 38, 18, 47, 0, 47, 44, 36, 0, 88, 0, 18, 79, 63, 5

Offset: 1

Author

Gus Wiseman, Jul 02 2018

Keywords

• nonn

Examples

			The a(24) = 8 partitions:
(14,10), (22,2),
(9,9,6), (12,9,3), (15,6,3), (18,3,3),
(8,8,4,4), (12,4,4,4).
		

Crossrefs

Cf. A000837, A067538, A074761, A289508, A289509, A290103, A316429, A316430, A316431, A316433.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],GCD@@#==Length[#]&]],{n,30}]

PARI

a(n) = {my(nb = 0); forpart(p=n, if (gcd(p)==#p, nb++);); nb;} \\ Michel Marcus, Jul 03 2018