A303362 - OEIS

A303362

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

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, 45, 50, 55, 58, 67, 78, 84, 95, 101, 113, 124, 137, 153, 169, 180, 198, 219, 242, 268, 291, 319, 342, 374, 412, 450, 492, 535, 573, 632, 685, 746, 813, 868, 944

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

LINKS

Fausto A. C. Cariboni, Table of n, a(n) for n = 1..450, (terms up to a(250) from Andrew Howroyd)

EXAMPLE

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

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&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(a(n, m=n, b=0)=

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));

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

} \\ Andrew Howroyd, Nov 02 2019

CROSSREFS

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

Sequence in context: A285779 A319320 A305194 * A362061 A183163 A338359

Adjacent sequences: A303359 A303360 A303361 * A303363 A303364 A303365

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 22 2018

STATUS

approved