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A303362 Number of strict integer partitions of n with pairwise indivisible parts. 51


%S 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 45,50,55,58,67,78,84,95,101,113,124,137,153,169,180,198,219,242,268,

%U 291,319,342,374,412,450,492,535,573,632,685,746,813,868,944

%N Number of strict integer partitions of n with pairwise indivisible parts.

%H 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 The a(14) = 7 strict integer partitions are (14), (11,3), (10,4), (9,5), (8,6), (7,5,2), (7,4,3).

%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&Select[Tuples[#,2],UnsameQ@@#&&Divisible@@#&]==={}&]],{n,60}]

%o (PARI)

%o lista(nn)={local(Cache=Map());

%o my(excl=vector(nn, n, sumdiv(n, d, 2^(n-d))));

%o my(a(n, m=n, b=0)=

%o if(n==0, 1,

%o while(m>n || bittest(b,0), m--; b>>=1);

%o my(hk=[n, m, b], z);

%o if(!mapisdefined(Cache, hk, &z),

%o z = if(m, self()(n, m-1, b>>1) + self()(n-m, m, bitor(b, excl[m])), 0);

%o mapput(Cache, hk, z)); z));

%o for(n=1, nn, print1(a(n), ", "))

%o } \\ _Andrew Howroyd_, Nov 02 2019

%Y Cf. A000009, A000837, A003238, A006126, A051424, A259936, A275307, A281116, A285572, A285573, A290103, A293606, A293993, A303364.

%K nonn

%O 1,5

%A _Gus Wiseman_, Apr 22 2018

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Last modified April 12 18:58 EDT 2021. Contains 342932 sequences. (Running on oeis4.)