A033637 - OEIS

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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

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

OFFSET

1,2

COMMENTS

Range of A000688.

LINKS

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

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 *)

PROG

(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

CROSSREFS

Cf. A046064.

Sequence in context: A033892 A033620 A376858 * A084034 A084347 A051038

Adjacent sequences: A033634 A033635 A033636 * A033638 A033639 A033640

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

STATUS

approved