A340828 Number of strict integer partitions of n whose maximum part is a multiple of their length.

1, 1, 2, 1, 2, 3, 3, 2, 4, 5, 6, 6, 7, 8, 11, 10, 13, 17, 18, 21, 24, 27, 30, 35, 39, 46, 53, 61, 68, 79, 87, 97, 110, 123, 139, 157, 175, 196, 222, 247, 278, 312, 347, 385, 433, 476, 531, 586, 651, 720, 800, 883, 979, 1085, 1200, 1325, 1464, 1614, 1777

Offset: 1

Author

Gus Wiseman, Feb 01 2021

Keywords

• nonn

Examples

			The a(1) = 1 through a(16) = 10 partitions (A..G = 10..16):
  1  2  3   4  5   6    7   8   9    A     B    C    D    E     F      G
        21     41  42   43  62  63   64    65   84   85   86    87     A6
                   321  61      81   82    83   A2   A3   A4    A5     C4
                                621  631   A1   642  C1   C2    C3     E2
                                     4321  632  651  643  653   E1     943
                                           641  921  652  932   654    952
                                                     931  941   942    961
                                                          8321  951    C31
                                                                C21    8431
                                                                8421   8521
                                                                54321
		

Links

• FindStat, St000010: The length of the partition.
• FindStat, St000147: The largest part of an integer partition.
• FindStat, St000784: The maximum of the length and the largest part of the integer partition.

Crossrefs

Note: A-numbers of Heinz-number sequences are in parentheses below.

The non-strict version is A168659 (A340609/A340610).

A018818 counts partitions into divisors (A326841).

A047993 counts balanced partitions (A106529).

A064173 counts partitions of positive/negative rank (A340787/A340788).

A067538 counts partitions whose length/max divides sum (A316413/A326836).

A072233 counts partitions by sum and length, with strict case A008289.

A096401 counts strict partition with length equal to minimum.

A102627 counts strict partitions with length dividing sum.

A326842 counts partitions whose length and parts all divide sum (A326847).

A326850 counts strict partitions whose maximum part divides sum.

A326851 counts strict partitions with length and maximum dividing sum.

A340829 counts strict partitions with Heinz number divisible by sum.

A340830 counts strict partitions with all parts divisible by length.

Cf. A003114, A006141, A064174, A117409, A143773 (A316428), A200750, A326843 (A326837), A330950 (A324851).

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&Divisible[Max@@#,Length[#]]&]],{n,30}]