A274240 Numbers n such that there is a smaller positive number j == n (mod 7) such that j*n is a square.

16, 25, 28, 32, 36, 48, 50, 56, 63, 64, 72, 75, 80, 81, 84, 96, 100, 108, 112, 121, 125, 126, 128, 140, 144, 150, 160, 162, 168, 169, 175, 176, 180, 189, 192, 196, 200, 208, 216, 224, 225, 240, 242, 243, 250, 252, 256, 272, 275, 280, 288, 289, 300, 304, 308

Offset: 1

Author

Vladimir Shevelev, Jun 15 2016

Keywords

• nonn

Comments

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).

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).

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

Examples

			25 is a member, since 4 == 25 (mod 7) and 4*25 is a square.
32 is a member, since 18 == 32 (mod 7) and 18*32 is a square.
		

Crossrefs

Cf. A046790, A274141, A274188.

Programs

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

Extensions

More terms from Felix Fröhlich, Jun 15 2016