A316432 - OEIS

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

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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}]