STATUS
proposed
approved
The OEIS is supported by the many generous donors to the OEIS Foundation.
Revision History for A371128
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing all changes.
Number of strict integer partitions of n containing all distinct divisors of all parts.
(history; published version)
(history; published version)
STATUS
editing
proposed
CROSSREFS
For partitions with no divisors of parts we have A303362, strict case of A305148, ranks A316476.
This is the strict Strict case of A371130 (ranks A370802) and A371178 (ranks A371177).
The Heinz numbers of these partitions are the squarefree terms of A371177.
A305148 counts partitions without divisors, strict A303362, ranks A316476.
Cf. A000837, A003963, A239312, A285573, A319055, `A355529, `A370803, A370808, A370813, A371168, A371171, A371172, A371173.
NAME
allocated for Gus WisemanNumber of strict integer partitions of n containing all distinct divisors of all parts.
DATA
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
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.
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.
For partitions with no divisors of parts we have A303362, strict case of A305148, ranks A316476.
The RHS is represented by A370820, for prime factors A303975.
This is the strict case of A371130 (ranks A370802) and A371178 (ranks A371177).
The Heinz numbers of these partitions are the squarefree terms of A371177.
The complement is counted by A371180, non-strict A371132.
A000005 counts divisors.
A000041 counts integer partitions, strict A000009.
A008284 counts partitions by length.
Cf. A000837, A003963, A239312, A285573, A319055, A355529, A370803, A370808, A370813, A371168, A371171, A371172, A371173.
KEYWORD
allocated
nonn
AUTHOR
Gus Wiseman, Mar 18 2024
STATUS
approved
editing
NAME
allocated for Gus Wiseman
KEYWORD
allocated
STATUS
approved