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A303362
Number of strict integer partitions of n with pairwise indivisible parts.
56
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
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 22 2018
STATUS
approved