The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A304709

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A304709

Number of integer partitions of n whose distinct parts are pairwise coprime.
(history; published version)

#15 by Susanna Cuyler at Sat Nov 02 19:59:11 EDT 2019

STATUS

proposed

approved

#14 by Andrew Howroyd at Sat Nov 02 19:26:26 EDT 2019

STATUS

editing

proposed

#13 by Andrew Howroyd at Sat Nov 02 19:26:19 EDT 2019

PROG

my(bc(n, m, b)=

my(a(n)=bc(n, n, 0) + 1 - numdiv(n));

STATUS

proposed

editing

#12 by Andrew Howroyd at Sat Nov 02 18:32:09 EDT 2019

STATUS

editing

proposed

#11 by Andrew Howroyd at Sat Nov 02 14:54:10 EDT 2019

LINKS

Andrew Howroyd, <a href="/A304709/b304709.txt">Table of n, a(n) for n = 1..500</a>

FORMULA

a(n) = A304712(n) + 1 - A000005(n). - Andrew Howroyd, Nov 02 2019

PROG

(PARI)

lista(nn)={local(Cache=Map());

my(excl=vector(nn, n, sum(i=1, n-1, if(gcd(i, n)>1, 2^(n-i)))));

my(b(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)=b(n, n, 0) + 1 - numdiv(n));

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

} \\ Andrew Howroyd, Nov 02 2019

CROSSREFS

Cf. A000005, A007359, A007360, A018783, A051424, A078374, A101268, A289508, A289509, A302569, A302696, A302698, A302796, A302797, A304711, A304712.

STATUS

approved

editing

#10 by Bruno Berselli at Mon May 21 03:26:03 EDT 2018

STATUS

reviewed

approved

#9 by Joerg Arndt at Sun May 20 10:40:24 EDT 2018

STATUS

proposed

reviewed

#8 by Gus Wiseman at Fri May 18 19:08:19 EDT 2018

STATUS

editing

proposed

#7 by Gus Wiseman at Fri May 18 19:08:07 EDT 2018

EXAMPLE

The a(6) = 7 integer partitions of 6 whose distinct parts are pairwise coprime are (51), (411), (321), (3111), (2211), (21111), (111111).

#6 by Gus Wiseman at Fri May 18 19:07:35 EDT 2018

EXAMPLE

The a(6) = 7 integer partitions whose distinct parts are pairwise coprime are (51), (411), (321), (3111), (2211), (21111), (111111).

STATUS

proposed

editing