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A303362 Number of strict integer partitions of n with pairwise indivisible parts.

%I A303362 #16 Dec 16 2020 08:45:31
%S A303362 1,1,1,1,2,1,3,2,3,4,5,4,6,7,7,9,11,12,13,15,17,20,23,25,27,32,35,40,
%T A303362 45,50,55,58,67,78,84,95,101,113,124,137,153,169,180,198,219,242,268,
%U A303362 291,319,342,374,412,450,492,535,573,632,685,746,813,868,944
%N A303362 Number of strict integer partitions of n with pairwise indivisible parts.
%H A303362 Fausto A. C. Cariboni, <a href="/A303362/b303362.txt">Table of n, a(n) for n = 1..450</a>, (terms up to a(250) from Andrew Howroyd)
%e A303362 The a(14) = 7 strict integer partitions are (14), (11,3), (10,4), (9,5), (8,6), (7,5,2), (7,4,3).
%t A303362 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&Select[Tuples[#,2],UnsameQ@@#&&Divisible@@#&]==={}&]],{n,60}]
%o A303362 (PARI)
%o A303362 lista(nn)={local(Cache=Map());
%o A303362   my(excl=vector(nn, n, sumdiv(n, d, 2^(n-d))));
%o A303362   my(a(n, m=n, b=0)=
%o A303362      if(n==0, 1,
%o A303362         while(m>n || bittest(b,0), m--; b>>=1);
%o A303362         my(hk=[n, m, b], z);
%o A303362         if(!mapisdefined(Cache, hk, &z),
%o A303362           z = if(m, self()(n, m-1, b>>1) + self()(n-m, m, bitor(b, excl[m])), 0);
%o A303362           mapput(Cache, hk, z)); z));
%o A303362    for(n=1, nn, print1(a(n), ", "))
%o A303362 } \\ _Andrew Howroyd_, Nov 02 2019
%Y A303362 Cf. A000009, A000837, A003238, A006126, A051424, A259936, A275307, A281116, A285572, A285573, A290103, A293606, A293993, A303364.
%K A303362 nonn
%O A303362 1,5
%A A303362 _Gus Wiseman_, Apr 22 2018