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A331379 Number of integer partitions of n whose sum of primes of parts is divisible by n. 17
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, 167, 193, 232, 253, 300, 342, 427, 469, 557, 628, 729, 846, 936, 1088, 1195, 1450, 1601, 1895, 2097, 2482, 2782, 3220, 3592, 4073, 4641, 5202, 5911, 6494, 7443, 8294 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

LINKS

Table of n, a(n) for n=1..56.

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.

Cf. A000040, A001414, A056239, A324850, A330954, A331378, A331382.

Sequence in context: A058184 A087777 A030118 * A023835 A272633 A240817

Adjacent sequences:  A331376 A331377 A331378 * A331380 A331381 A331382

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 17 2020

STATUS

approved

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Last modified September 25 23:23 EDT 2020. Contains 337346 sequences. (Running on oeis4.)