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A195085 Positive integers n for which there exist exactly two integers k in {1,2,3,...,n-1} such that k*n is square.

%I A195085 #16 Sep 08 2022 08:45:59
%S A195085 9,18,27,45,54,63,90,99,117,126,135,153,171,189,198,207,234,261,270,
%T A195085 279,297,306,315,333,342,351,369,378,387,414,423,459,477,495,513,522,
%U A195085 531,549,558,585,594,603,621,630,639,657,666,693,702,711,738,747,765,774,783
%N A195085 Positive integers n for which there exist exactly two integers k in {1,2,3,...,n-1} such that k*n is square.
%C A195085 It appears that the terms of this sequence are exactly 9 times those of A005117 and (9/4) times those of A133466.
%C A195085 Also, this sequence gives the positions of those terms where A057918(n)=2.
%H A195085 Reinhard Zumkeller, <a href="/A195085/b195085.txt">Table of n, a(n) for n = 1..1000</a>
%e A195085 Given n=9, {1*9, 2*9, ..., 8*9} = {9,18,27,36,45,54,63,72}, of which 9 and 36 are square. Thus 9 is a term of the sequence.
%o A195085 (Haskell)
%o A195085 a195085 n = a195085_list !! (n-1)
%o A195085 a195085_list = map (+ 1) $ elemIndices 2 a057918_list
%o A195085 -- _Reinhard Zumkeller_, Mar 27 2012
%o A195085 (Magma) [k:k in [1..800]|#[m:m in [1..k-1]| IsSquare(m*k)] eq 2]; // _Marius A. Burtea_, Dec 03 2019
%Y A195085 Cf. A005117, A057918, A133466.
%K A195085 nonn
%O A195085 1,1
%A A195085 _John W. Layman_, Sep 08 2011