OFFSET

0,6

EXAMPLE

The a(n) partitions for n = 1, 5, 7, 8, 9, 13, 14:

1 221 43 311111 63 7411 65111

311 511 11111111 441 721111 322211111

11111 3211 711 43111111 311111111111

22111 42111 421111111 11111111111111

1111111 2211111 3211111111

111111111 22111111111

1111111111111

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], Divisible[Plus@@Prime/@#, Times@@#]&]], {n, 0, 30}]

CROSSREFS

The Heinz numbers of these partitions are given by A331382.

Numbers divisible by the sum of their prime factors are A036844.

Partitions whose product is divisible by their sum are A057568.

Numbers divisible by the sum of their prime indices are A324851.

Product of prime indices is divisible by sum of prime indices: A326149.

Partitions whose Heinz number is divisible by their sum are A330950.

Sum of prime factors is divisible by sum of prime indices: A331380

Partitions whose product is equal to their sum of primes are A331383.

Product of prime indices equals sum of prime factors: A331384.

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 16 2020

STATUS

approved