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 A330953 Number of integer partitions of n whose Heinz number (product of primes of parts) is divisible by their sum of primes of parts. 18
 1, 2, 1, 2, 1, 3, 3, 4, 6, 3, 12, 10, 12, 14, 27, 38, 44, 52, 48, 77, 101, 106, 127, 206, 268, 377, 392, 496, 602, 671, 821, 1090, 1318, 1568, 1926, 2260, 2703, 3258, 3942, 4858, 5923, 6891, 8286, 9728, 11676, 13775, 16314, 19749, 23474, 27793, 32989, 38775 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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(11) = 12 partitions: (A = 10, B = 11):   1  2   3  4     5  6    7      8         9        A         B      11     1111     222  3211   431       432      5311      542                      321  22111  4211      3321     22111111  5411                                  11111111  32211              33221                                            321111             42221                                            2211111            53111                                                               322211                                                               431111                                                               521111                                                               2222111                                                               3311111                                                               32111111 For example, the partition (3,3,2,2,1) is counted under a(11) because 5*5*3*3*2 = 450 is divisible by 5+5+3+3+2 = 18. MATHEMATICA Table[Length[Select[IntegerPartitions[n], Divisible[Times@@Prime/@#, Plus@@Prime/@#]&]], {n, 30}] CROSSREFS The Heinz numbers of these partitions are given by A036844. Numbers divisible by the sum of their prime indices are 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. Partitions whose Heinz number is divisible by their sum are A330950. Partitions whose product is divisible by their sum of primes are A330954. Cf. A001414, A003963, A056239, A112798, A120383, A326149, A326155, A331378, A331379, A331381, A331383, A331415, A331416, A331417. Sequence in context: A029174 A058753 A282249 * A325702 A304746 A304748 Adjacent sequences:  A330950 A330951 A330952 * A330954 A330955 A330956 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.)