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

1,10

Links

Table of n, a(n) for n=1..77.

Example

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).

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A136166 A259525 A319071 * A046522 A242896 A240183

Adjacent sequences: A316429 A316430 A316431 * A316433 A316434 A316435

Keyword

nonn

Author

Gus Wiseman, Jul 02 2018

Status

approved