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A371128 revision #4

A371128

Number of strict integer partitions of n containing all distinct divisors of all parts.

1, 1, 0, 1, 1, 0, 2, 1, 2, 1, 2, 2, 3, 3, 3, 5, 3, 5, 6, 7, 7, 8, 8, 9, 12, 13, 13, 14, 15, 16, 19, 23, 25, 26, 26, 27, 36, 37, 40, 42, 46, 50, 55, 66, 65, 71, 71, 82, 90, 102, 103, 114, 117, 130, 147, 154, 166, 176, 182, 194, 228, 239, 259, 267, 287, 307, 336

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OFFSET

0,7

COMMENTS

Also strict integer partitions such that the number of parts is equal to the number of distinct divisors of all parts.

LINKS

Table of n, a(n) for n=0..66.

EXAMPLE

The a(9) = 1 through a(19) = 7 partitions (A..H = 10..17):

531 721 731 B1 751 D1 B31 D21 B51 H1 B71

4321 5321 5421 931 B21 7521 7531 D31 9531 D51

6321 7321 7421 8421 64321 B321 A521 B521

9321 65321 B421 D321

54321 74321 75321 75421

84321 76321

94321

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&SubsetQ[#, Union@@Divisors/@#]&]], {n, 0, 30}]

CROSSREFS

The LHS is represented by A001221, distinct case of A001222.

The RHS is represented by A370820, for prime factors A303975.

Strict case of A371130 (ranks A370802) and A371178 (ranks A371177).

The complement is counted by A371180, non-strict A371132.

A000005 counts divisors.

A000041 counts integer partitions, strict A000009.

A008284 counts partitions by length.

A305148 counts partitions without divisors, strict A303362, ranks A316476.

Cf. A000837, A003963, A239312, A285573, A319055, A370803, A370808, A371171, A371172, A371173.

Sequence in context: A058774 A033101 A220413 * A029217 A161230 A161054

Adjacent sequences: A371125 A371126 A371127 * A371129 A371130 A371131

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 18 2024

STATUS

editing