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%I #11 Mar 16 2024 16:49:34
%S 1,5,9,13,14,17,20,21,24,25,26,29,32,33,34,37,38,41,44,45,48,49,50,53,
%T 54,56,57,61,62,64,65,68,69,73,74,76,77,80,81,84,85,86,89,90,92,93,94,
%U 97,98,101,104,105,109,110,113,114,116,117,118,120,121,122
%N Numbers k >= 1 for which k!!/Sum_{i=1..k} k is an integer.
%H Jayanta Basu, <a href="/A130333/b130333.txt">Table of n, a(n) for n = 0..1000</a>
%e 5!! = 5*3*1 = 15; 5+4+3+2+1 = 15; 15/15 = 1.
%e 13!! = 13*11*9*7*5*3*1 = 135135; 13+12+11+10+9+8+7+6+5+4+3+2+1 = 91; 135135/91 = 1485.
%p P:=proc(n) local a,i,j,k,w; for i from 1 by 1 to n do k:=i; w:=i-2; while w>0 do k:=k*w; w:=w-2; od; j:=sum('w','w'=1..i); a:=k/j; if trunc(a)=a then print(i) fi; od; end: P(100);
%t pr[n_] := Times @@ If[OddQ[n], Range[1, n, 2], Range[2, n, 2]]; Select[Range[122], Divisible[pr[#], Total[Range[#]]] &] (* _Jayanta Basu_, Aug 11 2013 *)
%t Select[Range[200],Divisible[#!!,(#(#+1))/2]&] (* _Harvey P. Dale_, Feb 09 2015 *)
%Y Cf. A130319, A130332.
%K easy,nonn
%O 0,2
%A _Paolo P. Lava_ and _Giorgio Balzarotti_, May 24 2007
%E More terms from _Jayanta Basu_, Aug 11 2013
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