

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
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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



FORMULA



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.
Pairwise indivisible partitions are A303362.
Strict, relatively prime partitions are A078374.
A ranking function using binary indices is A328671.


KEYWORD

nonn


AUTHOR



STATUS

approved



