cp's OEIS Frontend

A331379 Number of integer partitions of n whose sum of primes of parts is divisible by n.

%I A331379 #5 Jan 17 2020 17:41:16
%S A331379 1,1,1,1,1,1,2,4,6,7,7,7,9,11,18,24,33,39,44,51,55,66,83,106,121,145,
%T A331379 167,193,232,253,300,342,427,469,557,628,729,846,936,1088,1195,1450,
%U A331379 1601,1895,2097,2482,2782,3220,3592,4073,4641,5202,5911,6494,7443,8294
%N A331379 Number of integer partitions of n whose sum of primes of parts is divisible by n.
%e A331379 The a(6) = 1 through a(11) = 7 partitions:
%e A331379   111111  52       53        54         64          641
%e A331379           1111111  62        63         541         5411
%e A331379                    521       531        631         6311
%e A331379                    11111111  621        5311        53111
%e A331379                              5211       6211        62111
%e A331379                              111111111  52111       521111
%e A331379                                         1111111111  11111111111
%e A331379 For example, the partition (5,4,1,1) has sum of primes 11+7+2+2 = 22, which is divisible by 5+4+1+1 = 11, so (5,4,1,1) is counted under a(11).
%t A331379 Table[Length[Select[IntegerPartitions[n],Divisible[Plus@@Prime/@#,n]&]],{n,30}]
%Y A331379 The Heinz numbers of these partitions are given by A331380.
%Y A331379 Numbers divisible by the sum of their prime factors are A036844.
%Y A331379 Partitions whose product is divisible by their sum are A057568.
%Y A331379 Numbers divisible by the sum of their prime indices are A324851.
%Y A331379 Product of prime indices is divisible by sum of prime indices: A326149.
%Y A331379 Partitions whose Heinz number is divisible by their sum are A330950.
%Y A331379 Partitions whose Heinz number is divisible by their sum of primes: A330953.
%Y A331379 Partitions whose product divides their sum of primes are A331381.
%Y A331379 Partitions whose product is equal to their sum of primes are A331383.
%Y A331379 Product of prime indices equals sum of prime factors: A331384.
%Y A331379 Cf. A000040, A001414, A056239, A324850, A330954, A331378, A331382.
%K A331379 nonn
%O A331379 1,7
%A A331379 _Gus Wiseman_, Jan 17 2020