A033637 Products of partition numbers A000041(n).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 49, 50, 54, 55, 56, 60, 63, 64, 66, 70, 72, 75, 77, 80, 81, 84, 88, 90, 96, 98, 99, 100, 101, 105, 108, 110, 112, 120, 121, 125, 126, 128, 132, 135, 140

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Range of A000688.

Links

• David W. Wilson, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046064.

Programs

Maple

with(combinat): A000041:=proc(n) options remember: RETURN(numbpart(n)): end: partdiv:=proc(m,i) local j,q,f: f:=0: for j from i by -1 to 2 while(f=0) do if(irem(m, A000041(j))=0) then q:=iquo(m, A000041(j)): if(q=1) then RETURN(1) else f:=partdiv(q,j) fi fi od: RETURN(f): end: for i from 2 to 15 do for n from A000041(i) to A000041(i+1)-1 do m:=partdiv(n,i): if m=1 then printf("%d, ",n) fi od od: # C. Ronaldo

Mathematica

p0 = Table[ PartitionsP[n], {n, 1, 40 (* ~ 1148 terms *)}] ; f[p_] := Select[ Outer[Times, p, p] // Flatten // Union, # <= Last[p0] &]; FixedPoint[f, p0] (* Jean-François Alcover, Oct 03 2013 *)

PARI

is(n,mx=n)=if(n>>valuation(n,2)==1,return(1));for(i=3,n, my(p=numbpart(i),m=n); while(m%p==0, if(is(m/=p),return(1))); if(p>n, return(0))) \\ Charles R Greathouse IV, Jun 28 2013

Extensions

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 02 2005