cp's OEIS Frontend

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

%I A340828 #10 Feb 08 2021 03:05:59
%S A340828 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,
%T A340828 61,68,79,87,97,110,123,139,157,175,196,222,247,278,312,347,385,433,
%U A340828 476,531,586,651,720,800,883,979,1085,1200,1325,1464,1614,1777
%N A340828 Number of strict integer partitions of n whose maximum part is a multiple of their length.
%H A340828 FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000010">St000010: The length of the partition.</a>
%H A340828 FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000147">St000147: The largest part of an integer partition.</a>
%H A340828 FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000784">St000784: The maximum of the length and the largest part of the integer partition.</a>
%e A340828 The a(1) = 1 through a(16) = 10 partitions (A..G = 10..16):
%e A340828   1  2  3   4  5   6    7   8   9    A     B    C    D    E     F      G
%e A340828         21     41  42   43  62  63   64    65   84   85   86    87     A6
%e A340828                    321  61      81   82    83   A2   A3   A4    A5     C4
%e A340828                                 621  631   A1   642  C1   C2    C3     E2
%e A340828                                      4321  632  651  643  653   E1     943
%e A340828                                            641  921  652  932   654    952
%e A340828                                                      931  941   942    961
%e A340828                                                           8321  951    C31
%e A340828                                                                 C21    8431
%e A340828                                                                 8421   8521
%e A340828                                                                 54321
%t A340828 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&Divisible[Max@@#,Length[#]]&]],{n,30}]
%Y A340828 Note: A-numbers of Heinz-number sequences are in parentheses below.
%Y A340828 The non-strict version is A168659 (A340609/A340610).
%Y A340828 A018818 counts partitions into divisors (A326841).
%Y A340828 A047993 counts balanced partitions (A106529).
%Y A340828 A064173 counts partitions of positive/negative rank (A340787/A340788).
%Y A340828 A067538 counts partitions whose length/max divides sum (A316413/A326836).
%Y A340828 A072233 counts partitions by sum and length, with strict case A008289.
%Y A340828 A096401 counts strict partition with length equal to minimum.
%Y A340828 A102627 counts strict partitions with length dividing sum.
%Y A340828 A326842 counts partitions whose length and parts all divide sum (A326847).
%Y A340828 A326850 counts strict partitions whose maximum part divides sum.
%Y A340828 A326851 counts strict partitions with length and maximum dividing sum.
%Y A340828 A340829 counts strict partitions with Heinz number divisible by sum.
%Y A340828 A340830 counts strict partitions with all parts divisible by length.
%Y A340828 Cf. A003114, A006141, A064174, A117409, A143773 (A316428), A200750, A326843 (A326837), A330950 (A324851).
%K A340828 nonn
%O A340828 1,3
%A A340828 _Gus Wiseman_, Feb 01 2021