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A303364 Number of strict integer partitions of n with pairwise indivisible and squarefree parts. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 22 13:59 EST 2021. Contains 340362 sequences. (Running on oeis4.)