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 A328678 Number of strict, pairwise indivisible, relatively prime integer partitions of n. 2
 1, 0, 0, 0, 1, 0, 2, 1, 2, 2, 4, 3, 5, 4, 5, 7, 10, 9, 12, 11, 14, 15, 22, 20, 25, 26, 32, 33, 44, 41, 54, 49, 62, 67, 80, 80, 100, 100, 118, 121, 152, 148, 179, 178, 210, 219, 267, 259, 316, 313, 363, 380, 449, 448, 529, 532, 619, 640, 745, 749, 867, 889 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS Note that pairwise indivisibility implies strictness, but we include "strict" in the name in order to more clearly distinguish it from A328676 = "Number of relatively prime integer partitions of n whose distinct parts are pairwise indivisible". LINKS Table of n, a(n) for n=1..62. FORMULA Moebius transform of A303362. EXAMPLE The a(1) = 1 through a(20) = 11 partitions (A..H = 10..20) (empty columns not shown): 1 32 43 53 54 73 65 75 76 95 87 97 98 B7 A9 B9 52 72 532 74 543 85 B3 B4 B5 A7 D5 B8 D7 83 732 94 743 D2 D3 B6 765 C7 H3 92 A3 752 654 754 C5 873 D6 875 B2 753 853 D4 954 E5 965 952 E3 972 F4 974 B32 F2 B43 G3 A73 764 B52 H2 B54 A43 D32 865 B72 7532 964 D43 B53 D52 7543 MATHEMATICA stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}]; Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&GCD@@#==1&&stableQ[#, Divisible]&]], {n, 30}] CROSSREFS The Heinz numbers of these partitions are the squarefree terms of A328677. The non-strict case is A328676. Pairwise indivisible partitions are A303362. Strict, relatively prime partitions are A078374. A ranking function using binary indices is A328671. Cf. A000837, A285572, A285573, A304713, A305148, A316476, A328171. Sequence in context: A332718 A341461 A337485 * A184199 A262346 A242560 Adjacent sequences: A328675 A328676 A328677 * A328679 A328680 A328681 KEYWORD nonn AUTHOR Gus Wiseman, Oct 30 2019 STATUS approved

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Last modified August 8 04:35 EDT 2024. Contains 375018 sequences. (Running on oeis4.)