A236652 Positive integers n such that n^2 divided by the digital root of n is a square.

1, 4, 9, 10, 18, 19, 22, 27, 28, 36, 37, 40, 45, 46, 54, 55, 58, 63, 64, 72, 73, 76, 81, 82, 90, 91, 94, 99, 100, 108, 109, 112, 117, 118, 126, 127, 130, 135, 136, 144, 145, 148, 153, 154, 162, 163, 166, 171, 172, 180, 181, 184, 189, 190, 198, 199, 202, 207

Offset: 1

Author

Colin Barker, Jan 29 2014

Keywords

• nonn
• base
• easy

Examples

			18 is in the sequence because the digital root of 18 is 9, and 18^2/9 = 36 = 6^2.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Crossrefs

Cf. A010888, A236653.

Programs

PARI

s=[]; for(n=1, 300, d=(n-1)%9+1; if(n^2%d==0 && issquare(n^2\d), s=concat(s, n))); s

PARI

Vec(x*(8*x^4+x^3+5*x^2+3*x+1)/((x-1)^2*(x^4+x^3+x^2+x+1)) + O(x^100))

Formula

a(n) = a(n-1)+a(n-5)-a(n-6).

G.f.: x*(8*x^4+x^3+5*x^2+3*x+1) / ((x-1)^2*(x^4+x^3+x^2+x+1)).