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

1,5

Links

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

Example

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).

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A220272 A298917 A322530 * A131332 A059780 A075119

Adjacent sequences: A303361 A303362 A303363 * A303365 A303366 A303367

Keyword

nonn

Author

Gus Wiseman, Apr 22 2018

Status

approved