OFFSET

1,7

EXAMPLE

The a(6) = 1 through a(11) = 7 partitions:

111111 52 53 54 64 641

1111111 62 63 541 5411

521 531 631 6311

11111111 621 5311 53111

5211 6211 62111

111111111 52111 521111

1111111111 11111111111

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).

MATHEMATICA

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

CROSSREFS

The Heinz numbers of these partitions are given by A331380.

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.

Partitions whose Heinz number is divisible by their sum of primes: A330953.

Partitions whose product divides their sum of primes are A331381.

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 17 2020

STATUS

approved