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A046791 A046790 has several definitions, one of which is: "Numbers i such that there is a smaller positive number j such that (i+j)/2 and sqrt(i*j) are integers". The present sequence gives the smallest choice for j.

%I A046791 #48 Oct 19 2017 10:38:25
%S A046791 2,1,4,2,6,1,3,2,4,10,5,12,1,2,6,14,7,4,2,3,20,1,22,10,6,2,11,4,26,12,
%T A046791 28,13,30,1,5,14,2,15,34,4,3,6,38,17,10,2,42,1,19,7,44,20,46,21,12,4,
%U A046791 22,2,23,52,6,14,1,58,26,60,2,3,5,62,10,28,4,29,66,30,68,11,31,70,2,1,6,74,33
%N A046791 A046790 has several definitions, one of which is: "Numbers i such that there is a smaller positive number j such that (i+j)/2 and sqrt(i*j) are integers". The present sequence gives the smallest choice for j.
%C A046791 Note that A046790 is the complement of A078779. - _Omar E. Pol_, Jun 11 2016
%H A046791 David A. Corneth, <a href="/A046791/b046791.txt">Table of n, a(n) for n = 1..10000</a>
%F A046791 Let b(n)=A046790(n). Let k=k(n) be the greatest number whose square divides b(n) and is such that b(n) and b(n)/k^2 are of the same parity. Then a(n) = b(n)/k^2. - _Vladimir Shevelev_, Jun 07 2016
%F A046791 Or, equivalently, a(n) is the squarefree part s(n) of b(n), if either b(n) is odd or s(n) is even. Otherwise, when b(n) is even, but s(n) is odd, a(n)=4*s(n). - _David A. Corneth_, Jun 07 2016
%e A046791 From _Vladimir Shevelev_, Jun 07 2016: (Start)
%e A046791 A046790(5)=24 with even squarefree part (6), so a(5) = 6;
%e A046791 A046790(12)=48 with odd squarefree part (3), so a(12) = 3*4=12.
%e A046791 (End)
%o A046791 (PARI) a(n) = my(n=A046790(n),f=factor(n),p=n%2);f[,2]=f[,2]%2;r=prod(i=1,matsize(f)[1],f[i,1]^f[i,2]);r*=(4^(n%2==0&&r%2==1)) \\ _David A. Corneth_, Jun 07 2016
%Y A046791 Cf. A046790.
%K A046791 nonn
%O A046791 1,1
%A A046791 _David W. Wilson_, Dec 11 1999
%E A046791 Entry revised by _N. J. A. Sloane_, with help from _Don Reble_ and several OEIS editors. Jun 07 2016