A303364 Number of strict integer partitions of n with pairwise indivisible and squarefree parts.

1, 1, 1, 0, 2, 1, 2, 1, 1, 3, 2, 2, 4, 3, 3, 4, 6, 5, 5, 6, 7, 8, 9, 10, 10, 11, 11, 14, 14, 17, 16, 18, 19, 23, 24, 27, 29, 30, 33, 36, 41, 41, 42, 46, 51, 56, 60, 66, 67, 71, 81, 86, 93, 96, 101, 110, 121, 129, 135, 144, 153, 159, 173, 192, 204, 207, 224

Offset: 1

Author

Gus Wiseman, Apr 22 2018

Keywords

• nonn

Examples

			The a(23) = 9 strict integer partitions are (23), (13,10), (17,6), (21,2), (10,7,6), (11,7,5), (13,7,3), (11,7,3,2), (13,5,3,2).
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 1..700 (terms 0..400 from Andrew Howroyd)

Crossrefs

Cf. A000009, A000837, A003238, A005117, A006126, A051424, A073576, A285572, A285573, A293606, A293993, A303362, A303365.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&And@@SquareFreeQ/@#&&Select[Tuples[#,2],UnsameQ@@#&&Divisible@@#&]==={}&]],{n,60}]

PARI

lista(nn)={local(Cache=Map());
  my(excl=vector(nn, n, sumdiv(n, d, 2^(n-d))));
  my(c(n, m, b)=
     if(n==0, 1,
        while(m>n || bittest(b,0), m--; b>>=1);
        my(hk=[n, m, b], z);
        if(!mapisdefined(Cache, hk, &z),
          z = if(m, self()(n, m-1, b>>1) + self()(n-m, m, bitor(b, excl[m])), 0);
          mapput(Cache, hk, z)); z));
  my(a(n)=c(n, n, sum(i=1, n, if(!issquarefree(i), 2^(n-i)))));
  for(n=1, nn, print1(a(n), ", "))
} \\ Andrew Howroyd, Nov 02 2019