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A046064 Not a product of partition numbers (A000041). 2


%S 13,17,19,23,26,29,31,34,37,38,39,41,43,46,47,51,52,53,57,58,59,61,62,

%T 65,67,68,69,71,73,74,76,78,79,82,83,85,86,87,89,91,92,93,94,95,97,

%U 102,103,104,106,107,109,111,113,114,115,116,117,118,119,122,123,124,127

%N Not a product of partition numbers (A000041).

%H G. K. Patil, <a href="https://web.archive.org/web/20150911053452/http://www.ijsres.com/2014/vol-1_issue-6/paper_8.pdf">Ramanujan's Life And His Contributions In The Field Of Mathematics</a>, International Journal of Scientific Research and Engineering Studies (IJSRES), 1(6) (2014), ISSN: 2349-8862.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AbelianGroup.html">Abelian Group</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PartitionFunctionPCongruences.html">Partition Function PCongruences</a>.

%p 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 14 do for n from A000041(i) to A000041(i+1)-1 do m:=partdiv(n,i): if m=0 then printf("%d, ",n) fi od od: # C. Ronaldo

%Y Cf. A000041, A046056, A046063, A033637.

%K nonn

%O 1,1

%A _Eric W. Weisstein_

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Last modified June 23 21:09 EDT 2021. Contains 345402 sequences. (Running on oeis4.)