A316433 Number of integer partitions of n whose length is equal to the LCM of all parts.

1, 0, 1, 1, 1, 0, 2, 1, 4, 3, 4, 4, 8, 5, 7, 8, 10, 8, 13, 13, 20, 18, 25, 25, 36, 34, 48, 52, 64, 64, 85, 85, 108, 106, 129, 133, 160, 158, 189, 194, 229, 228, 276, 279, 332, 336, 394, 402, 476, 489, 572, 599, 699, 728, 845, 889, 1032, 1094, 1251, 1332, 1523

Offset: 1

Author

Gus Wiseman, Jul 02 2018

Keywords

• nonn

Examples

			The a(13) = 8 partitions are (4441), (55111), (322222), (332221), (333211), (622111), (631111), (7111111).
		

Crossrefs

Cf. A067538, A074761, A143773, A285572, A289508, A290103, A305566, A316429, A316430, A316431, A316432.

Programs

Mathematica

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

PARI

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