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%I A331381 #6 Jan 17 2020 10:37:53
%S A331381 1,1,1,1,1,3,1,5,2,6,6,5,5,7,4,7,7,7,10,8,9,6,10,9,9,15,7,12,10,14,10,
%T A331381 10,8,8,15,10,7,16,13,9,10,14,12,10,8,14,11,13,11,16,15,14,15,15,10,
%U A331381 14,18,11,12,13,13,18,21,15,16,19,16,15,8,17,17
%N A331381 Number of integer partitions of n whose sum of primes of parts is divisible by their product of parts.
%e A331381 The a(n) partitions for n = 1, 5, 7, 8, 9, 13, 14:
%e A331381   1  221    43       311111    63         7411           65111
%e A331381      311    511      11111111  441        721111         322211111
%e A331381      11111  3211               711        43111111       311111111111
%e A331381             22111              42111      421111111      11111111111111
%e A331381             1111111            2211111    3211111111
%e A331381                                111111111  22111111111
%e A331381                                           1111111111111
%t A331381 Table[Length[Select[IntegerPartitions[n],Divisible[Plus@@Prime/@#,Times@@#]&]],{n,0,30}]
%Y A331381 The Heinz numbers of these partitions are given by A331382.
%Y A331381 Numbers divisible by the sum of their prime factors are A036844.
%Y A331381 Partitions whose product is divisible by their sum are A057568.
%Y A331381 Numbers divisible by the sum of their prime indices are A324851.
%Y A331381 Product of prime indices is divisible by sum of prime indices: A326149.
%Y A331381 Partitions whose Heinz number is divisible by their sum are A330950.
%Y A331381 Sum of prime factors is divisible by sum of prime indices: A331380
%Y A331381 Partitions whose product is equal to their sum of primes are A331383.
%Y A331381 Product of prime indices equals sum of prime factors: A331384.
%Y A331381 Cf. A000040, A001414, A324850, A330953, A330954, A331378, A331379, A331415, A331416.
%K A331381 nonn
%O A331381 0,6
%A A331381 _Gus Wiseman_, Jan 16 2020

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