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

1,7

Links

Table of n, a(n) for n=1..61.

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A231898 A276638 A116449 * A071046 A324757 A144334

Adjacent sequences: A316430 A316431 A316432 * A316434 A316435 A316436

Keyword

nonn

Author

Gus Wiseman, Jul 02 2018

Status

approved