A274188 Number n such that there is a smaller positive number j == n (mod 5) such that sqrt(j*n) is an integer.

9, 16, 18, 20, 27, 32, 36, 40, 45, 48, 49, 54, 60, 63, 64, 72, 80, 81, 90, 96, 98, 99, 100, 108, 112, 117, 120, 121, 125, 126, 128, 135, 140, 144, 147, 153, 160, 162, 169, 171, 176, 180, 189, 192, 196, 198, 200, 207, 208, 216, 220, 224, 225, 234, 240, 242, 243, 245, 250

Offset: 1

Author

Vladimir Shevelev, Jun 12 2016

Keywords

• nonn
• easy

Comments

Or numbers n>=9 having a divisor t^2 > 1, where t=k/m, 1<= m < k, such that n == n/t^2 (mod 5).

Or positive numbers n such that if n == 0 (mod 5), then it divisible by 5^3 or by the square of some other prime; otherwise n divisible by k^2, such that there is a k_1, 0< k_1

A generalization see in our seqfan list from Jun 13 (correction Jun 14) 2016.

Examples

			9 is member, since 4 == 9 (mod 5) and 4*9 is a square;
32 is member, since 2 == 32 (mod 5) and 2*32 is a square;
45 is member, since 5 == 45 (mod 5) and 5*45 is a square.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046790, A274141.

Programs

Mathematica

Select[Range@ 250, Function[n, Count[Sqrt[# n] & /@ Select[Range[n - 1], Mod[#, 5] == Mod[n, 5] &], k_ /; IntegerQ@ k] > 0]] (* Michael De Vlieger, Jun 14 2016 *)

PARI

isok(n)=j = n-5; while (j >0, if (issquare(j*n), return (1)); j -= 5;); 0; \\ Michel Marcus, Jun 14 2016

PARI

is(n)=!issquarefree(n/if(n%5, if(n%4, 1, 4), 5)) \\ Charles R Greathouse IV, Jun 15 2016

Formula

Let A(x) be the number of a(n)<=x. Then A(x)/x ~ 1 - 149/(20*Pi^2) = 1 - 7.45/Pi^2 = 0.24515718... as x goes to infinity. - Vladimir Shevelev, Jun 15 2016; corrected by Charles R Greathouse IV, Jun 15 2016

Extensions

Corrected and extended by Michel Marcus, Jun 14 2016

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