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%I M0264 #33 Dec 31 2020 17:23:45
%S 1,1,2,2,3,3,4,5,5,6,8,9,10,11,10,13,17,19,21,22,21,24,32,37,37,38,40,
%T 45,55,65,69,66,64,75,86,100,113,107,106,122,145,165,174,167,162,179,
%U 222,253,255,255,255,273,328,373,376,369,377,406,476,553,569,537,529
%N Number of partitions of n into distinct and pairwise relatively prime parts.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Fausto A. C. Cariboni, <a href="/A007360/b007360.txt">Table of n, a(n) for n = 1..750</a> (terms 1..350 from Alois P. Heinz)
%H M. LeBrun & D. Hoey, <a href="/A007359/a007359.pdf">Emails</a>
%F a(n) = A051424(n)-A051424(n-2). - _Vladeta Jovovic_, Dec 11 2004
%e From _Gus Wiseman_, Sep 23 2019: (Start)
%e The a(1) = 1 through a(10) = 6 partitions (A = 10):
%e (1) (2) (3) (4) (5) (6) (7) (8) (9) (A)
%e (21) (31) (32) (51) (43) (53) (54) (73)
%e (41) (321) (52) (71) (72) (91)
%e (61) (431) (81) (532)
%e (521) (531) (541)
%e (721)
%e (End)
%t $RecursionLimit = 1000; b[n_, i_, s_] := b[n, i, s] = Module[{f}, If[n == 0 || i == 1, 1, If[i<2, 0, f = FactorInteger[i][[All, 1]]; b[n, i-1, Select[s, #<i&]] + If[i <= n && f ~Intersection~ s == {}, b[n-i, i-1, Select[s ~Union~ f, #<i&]], 0]]]]; a[n_] := b[n, n, {}] - b[n-2, n-2, {}]; Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Mar 20 2014, after _Alois P. Heinz_ *)
%t Table[Length[Select[IntegerPartitions[n],Length[#]==1||UnsameQ@@#&&CoprimeQ@@Union[#]&]],{n,0,30}] (* _Gus Wiseman_, Sep 23 2019 *)
%Y Number of partitions of n into relatively prime parts = A000837.
%Y The non-strict case is A051424.
%Y Strict relatively prime partitions are A078374.
%Y Cf. A007359, A038348, A084422, A186974, A187106, A303140, A302569, A303362, A304714, A320426, A320436.
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_ and _Mira Bernstein_, following a suggestion from _Marc LeBrun_.
%E More precise definition from _Vladeta Jovovic_, Dec 11 2004
%E More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 13 2005
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