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Numbers n such that there is a smaller positive number j == n (mod 7) such that j*n is a square.
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%I #15 Jun 26 2016 06:19:43

%S 16,25,28,32,36,48,50,56,63,64,72,75,80,81,84,96,100,108,112,121,125,

%T 126,128,140,144,150,160,162,168,169,175,176,180,189,192,196,200,208,

%U 216,224,225,240,242,243,250,252,256,272,275,280,288,289,300,304,308

%N Numbers n such that there is a smaller positive number j == n (mod 7) such that j*n is a square.

%C Or numbers n >= 16 having a divisor t^2 > 1, where t=k/m, 1 <= m < k, such that n == n/t^2 (mod 7).

%C Or positive numbers n such that if n == 0 (mod 7), then n is divisible by 7^3 or by the square of some other prime; otherwise n is divisible by k^2, such that there is a k_1, 0 < k_1 < k such that k_1^2 == k^2 (mod 7) (or, according to the comment in A130290, n is divisible by some k^2 >= 16).

%C For a generalization, see the seqfan list from Jun 13 (correction Jun 14) 2016.

%e 25 is a member, since 4 == 25 (mod 7) and 4*25 is a square.

%e 32 is a member, since 18 == 32 (mod 7) and 18*32 is a square.

%o (PARI) is(n) = for(j=1, n-1, if(Mod(j, 7)==n && issquare(j*n), return(1))); return(0) \\ _Felix Fröhlich_, Jun 15 2016

%Y Cf. A046790, A274141, A274188.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Jun 15 2016

%E More terms from _Felix Fröhlich_, Jun 15 2016