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 A340828 Number of strict integer partitions of n whose maximum part is a multiple of their length. 12
 1, 1, 2, 1, 2, 3, 3, 2, 4, 5, 6, 6, 7, 8, 11, 10, 13, 17, 18, 21, 24, 27, 30, 35, 39, 46, 53, 61, 68, 79, 87, 97, 110, 123, 139, 157, 175, 196, 222, 247, 278, 312, 347, 385, 433, 476, 531, 586, 651, 720, 800, 883, 979, 1085, 1200, 1325, 1464, 1614, 1777 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Table of n, a(n) for n=1..59. FindStat, St000010: The length of the partition. FindStat, St000147: The largest part of an integer partition. FindStat, St000784: The maximum of the length and the largest part of the integer partition. EXAMPLE The a(1) = 1 through a(16) = 10 partitions (A..G = 10..16): 1 2 3 4 5 6 7 8 9 A B C D E F G 21 41 42 43 62 63 64 65 84 85 86 87 A6 321 61 81 82 83 A2 A3 A4 A5 C4 621 631 A1 642 C1 C2 C3 E2 4321 632 651 643 653 E1 943 641 921 652 932 654 952 931 941 942 961 8321 951 C31 C21 8431 8421 8521 54321 MATHEMATICA Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Divisible[Max@@#, Length[#]]&]], {n, 30}] CROSSREFS Note: A-numbers of Heinz-number sequences are in parentheses below. The non-strict version is A168659 (A340609/A340610). A018818 counts partitions into divisors (A326841). A047993 counts balanced partitions (A106529). A064173 counts partitions of positive/negative rank (A340787/A340788). A067538 counts partitions whose length/max divides sum (A316413/A326836). A072233 counts partitions by sum and length, with strict case A008289. A096401 counts strict partition with length equal to minimum. A102627 counts strict partitions with length dividing sum. A326842 counts partitions whose length and parts all divide sum (A326847). A326850 counts strict partitions whose maximum part divides sum. A326851 counts strict partitions with length and maximum dividing sum. A340829 counts strict partitions with Heinz number divisible by sum. A340830 counts strict partitions with all parts divisible by length. Cf. A003114, A006141, A064174, A117409, A143773 (A316428), A200750, A326843 (A326837), A330950 (A324851). Sequence in context: A024376 A230128 A342095 * A123265 A104345 A244516 Adjacent sequences: A340825 A340826 A340827 * A340829 A340830 A340831 KEYWORD nonn AUTHOR Gus Wiseman, Feb 01 2021 STATUS approved

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Last modified February 28 19:33 EST 2024. Contains 370400 sequences. (Running on oeis4.)