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 A340693 Number of integer partitions of n where each part is a divisor of the number of parts. 7
 1, 1, 1, 2, 2, 3, 2, 5, 5, 7, 7, 10, 10, 14, 14, 17, 19, 24, 24, 32, 33, 42, 43, 58, 59, 75, 79, 98, 104, 124, 128, 156, 166, 196, 204, 239, 251, 292, 306, 352, 372, 426, 445, 514, 543, 616, 652, 745, 790, 896, 960, 1080, 1162, 1311, 1400, 1574, 1692, 1892 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The only strict partitions counted are (), (1), and (2,1). Is there a simple generating function? LINKS EXAMPLE The a(1) = 1 through a(9) = 7 partitions:   1  11  21   22    311    2211    331      2222      333          111  1111  2111   111111  2221     4211      4221                     11111          4111     221111    51111                                    211111   311111    222111                                    1111111  11111111  321111                                                       21111111                                                       111111111 MATHEMATICA Table[Length[Select[IntegerPartitions[n], And@@IntegerQ/@(Length[#]/#)&]], {n, 0, 30}] CROSSREFS Note: Heinz numbers are given in parentheses below. The reciprocal version is A143773 (A316428), with strict case A340830. The case where length also divides n is A326842 (A326847). The Heinz numbers of these partitions are A340606. The version for factorizations is A340851, with reciprocal version A340853. A018818 counts partitions of n into divisors of n (A326841). A047993 counts balanced partitions (A106529). A067538 counts partitions of n whose length/max divides n (A316413/A326836). A067539 counts partitions with integer geometric mean (A326623). A072233 counts partitions by sum and length. A168659 = partitions whose greatest part divides their length (A340609). A168659 = partitions whose length divides their greatest part (A340610). A326843 = partitions of n whose length and maximum both divide n (A326837). A330950 = partitions of n whose Heinz number is divisible by n (A324851). Cf. A000041, A003114, A006141, A033630, A064174, A074761, A102627, A200750, A237984, A298423, A340827. Sequence in context: A050323 A318286 A214646 * A275382 A199583 A157922 Adjacent sequences:  A340690 A340691 A340692 * A340694 A340695 A340696 KEYWORD nonn AUTHOR Gus Wiseman, Jan 23 2021 STATUS approved

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Last modified January 17 04:46 EST 2022. Contains 350378 sequences. (Running on oeis4.)