cp's OEIS Frontend

A340830 Number of strict integer partitions of n such that every part is a multiple of the number of parts.

%I A340830 #8 Feb 03 2021 09:09:08
%S A340830 1,1,1,1,1,2,1,2,1,3,1,3,1,4,1,4,1,6,1,5,2,6,1,8,1,7,4,7,1,12,1,8,6,9,
%T A340830 1,16,1,10,9,11,1,21,1,12,13,12,1,28,1,13,17,16,1,33,1,19,22,15,1,45,
%U A340830 1,16,28,25,1,47,1,28,34,18
%N A340830 Number of strict integer partitions of n such that every part is a multiple of the number of parts.
%F A340830 a(n) = Sum_{d|n} A008289(n/d, d).
%e A340830 The a(n) partitions for n = 1, 6, 10, 14, 18, 20, 24, 26, 30:
%e A340830   1   6     10    14     18      20     24       26      30
%e A340830       4,2   6,4   8,6    10,8    12,8   16,8     18,8    22,8
%e A340830             8,2   10,4   12,6    14,6   18,6     20,6    24,6
%e A340830                   12,2   14,4    16,4   20,4     22,4    26,4
%e A340830                          16,2    18,2   22,2     24,2    28,2
%e A340830                          9,6,3          14,10    14,12   16,14
%e A340830                                         12,9,3   16,10   18,12
%e A340830                                         15,6,3           20,10
%e A340830                                                          15,9,6
%e A340830                                                          18,9,3
%e A340830                                                          21,6,3
%e A340830                                                          15,12,3
%t A340830 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&And@@IntegerQ/@(#/Length[#])&]],{n,30}]
%Y A340830 Note: A-numbers of Heinz-number sequences are in parentheses below.
%Y A340830 The non-strict case is A143773 (A316428).
%Y A340830 The case where length divides sum also is A340827.
%Y A340830 The version for factorizations is A340851.
%Y A340830 Factorization of this type are counted by A340853.
%Y A340830 A018818 counts partitions into divisors (A326841).
%Y A340830 A047993 counts balanced partitions (A106529).
%Y A340830 A067538 counts partitions whose length/max divide sum (A316413/A326836).
%Y A340830 A072233 counts partitions by sum and length, with strict case A008289.
%Y A340830 A102627 counts strict partitions whose length divides sum.
%Y A340830 A326850 counts strict partitions whose maximum part divides sum.
%Y A340830 A326851 counts strict partitions with length and maximum dividing sum.
%Y A340830 A340828 counts strict partitions with length divisible by maximum.
%Y A340830 A340829 counts strict partitions with Heinz number divisible by sum.
%Y A340830 Cf. A114638, A168659, A326641, A326843 (A326837), A326849, A326852 (A326838), A330950 (A324851), A340852.
%K A340830 nonn
%O A340830 1,6
%A A340830 _Gus Wiseman_, Feb 02 2021