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 A330950 Number of integer partitions of n whose Heinz number (product of primes of parts) is divisible by n. 16
 1, 1, 1, 2, 2, 3, 3, 7, 7, 11, 11, 22, 15, 30, 42, 77, 42, 101, 56, 176, 176, 231, 135, 490, 490, 490, 792, 1002, 490, 1575, 627, 3010, 2436, 2436, 3718, 5604, 1958, 4565, 6842, 12310, 3718, 14883, 4565, 21637, 26015, 17977, 8349, 53174, 44583, 63261 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions. LINKS EXAMPLE The a(1) = 1 through a(10) = 11 partitions:   1  11  21  211   32   321    43    5111      522      631              1111  311  2211   421   32111     3222     3331                         21111  4111  41111     4221     4321                                      221111    22221    5311                                      311111    32211    32221                                      2111111   222111   33211                                      11111111  2211111  43111                                                         322111                                                         331111                                                         3211111                                                         31111111 For example, the Heinz number of (3,2) is 15, which is divisible by 5, so (3,2) is counted under a(5). MATHEMATICA Table[Length[Select[IntegerPartitions[n], Divisible[Times@@Prime/@#, n]&]], {n, 20}] CROSSREFS The Heinz numbers of these partitions are given by A324851. Partitions whose product is divisible by their sum are A057568. Partitions whose Heinz number is divisible by all parts are A330952. Partitions whose Heinz number is divisible by their product are A324925. Cf. A056239, A112798, A196050, A324850, A324924, A330953, A330954, A331379, A331381, A331383, A331384. Sequence in context: A324520 A307737 A309684 * A032060 A241385 A307736 Adjacent sequences:  A330947 A330948 A330949 * A330951 A330952 A330953 KEYWORD nonn AUTHOR Gus Wiseman, Jan 15 2020 STATUS approved

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Last modified September 26 01:25 EDT 2020. Contains 337346 sequences. (Running on oeis4.)