The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A083290 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A083290

Number of partitions of n into distinct parts which are coprime to n and which are also pairwise relatively prime.
(history; published version)

#11 by Alois P. Heinz at Sun Dec 12 15:58:53 EST 2021

STATUS

proposed

approved

#10 by Jean-François Alcover at Sun Dec 12 11:28:23 EST 2021

STATUS

editing

proposed

#9 by Jean-François Alcover at Sun Dec 12 11:27:52 EST 2021

MATHEMATICA

a[n_] := a[n] = If[n == 1, 1, Module[{ip}, ip = IntegerPartitions[n, All, Select[Range[n - 1], CoprimeQ[#, n] &]]; Length@Select[ip, Sort[#] == Union[#] && AllTrue[Subsets[#, {2}], CoprimeQ @@ # &] &]]];

Table[Print[n, " ", a[n]]; a[n], {n, 1, 80}] (* Jean-François Alcover, Dec 12 2021 *)

STATUS

approved

editing

Discussion

Sun Dec 12

11:28

Jean-François Alcover: Very slow

#8 by Alois P. Heinz at Tue Apr 20 16:52:52 EDT 2021

STATUS

reviewed

approved

#7 by Hugo Pfoertner at Tue Apr 20 13:04:39 EDT 2021

STATUS

proposed

reviewed

#6 by Andrew Howroyd at Tue Apr 20 12:56:18 EDT 2021

STATUS

editing

proposed

#5 by Andrew Howroyd at Tue Apr 20 12:14:49 EDT 2021

NAME

Number of partitions of n into distinct coprimes parts which are coprime to n, and which are also mutually pairwise relatively prime.

DATA

1, 0, 1, 1, 2, 1, 3, 2, 3, 2, 7, 2, 9, 3, 4, 5, 16, 3, 20, 4, 8, 7, 31, 5, 22, 9, 18, 9, 54, 4, 68, 16, 21, 16, 28, 11, 112, 20, 32, 18, 144, 9, 173, 22, 33, 40, 221, 19, 139, 25, 71, 43, 327, 25, 117, 47, 103, 80, 475, 18, 568, 90, 98, 122, 191, 29, 805, 93, 197, 44

COMMENTS

a(n) <= A036998(n); see A082415 for numbers m with a(m) = A036998(m).

LINKS

Andrew Howroyd, <a href="/A083290/b083290.txt">Table of n, a(n) for n = 1..200</a>

EXAMPLE

a(7) = 3: since 7 = 3+4 = 2+5 = 1+6=7; 7 = 1+2+4=1+2+2*2 does not count (A036998(7)=4).

(A036998(7)=4).

PROG

(PARI) a(n)={local(Cache=Map()); my(recurse(r, p, k)=my(hk=[r, p, k], z); if(!mapisdefined(Cache, hk, &z), z=if(k==0, r==0, self()(r, p, k-1) + if(gcd(p, k)==1, self()(r-k, p*k, min(r-k, k-1)))); mapput(Cache, hk, z)); z); recurse(n, n, n)} \\ Andrew Howroyd, Apr 20 2021

CROSSREFS

Cf. A000010, A000586, A007360.

EXTENSIONS

Terms a(31) and beyond from Andrew Howroyd, Apr 20 2021

STATUS

approved

editing

#4 by Russ Cox at Fri Mar 30 18:50:32 EDT 2012

AUTHOR

_Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Apr 23 2003

Discussion

Fri Mar 30

18:50

OEIS Server: https://oeis.org/edit/global/246

#3 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

KEYWORD

nonn,new

nonn

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystemsgmail.com), Apr 23 2003

#2 by N. J. A. Sloane at Thu Feb 19 03:00:00 EST 2004

NAME

Partitions Number of partitions of n into distinct coprimes to n, which are also mutually relatively prime.

KEYWORD

nonn,new

nonn