A236653 Positive integers n such that n^3 divided by the digital root of n is a cube.

1, 8, 10, 19, 26, 28, 37, 44, 46, 55, 62, 64, 73, 80, 82, 91, 98, 100, 109, 116, 118, 127, 134, 136, 145, 152, 154, 163, 170, 172, 181, 188, 190, 199, 206, 208, 217, 224, 226, 235, 242, 244, 253, 260, 262, 271, 278, 280, 289, 296, 298, 307, 314, 316, 325

Offset: 1

Author

Colin Barker, Jan 29 2014

Keywords

• nonn
• base
• easy

Examples

			26 is in the sequence because the digital root of 26 is 8, and 26^3/8 = 2197 = 13^2.
		

Links

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

Crossrefs

Cf. A010888, A236652.

Programs

Mathematica

LinearRecurrence[{1,0,1,-1},{1,8,10,19},60] (* Harvey P. Dale, Sep 15 2019 *)

PARI

s=[]; for(n=1, 400, d=(n-1)%9+1; if(n^3%d==0 && ispower(n^3\d, 3), s=concat(s, n))); s

PARI

Vec(x*(8*x^3+2*x^2+7*x+1)/((x-1)^2*(x^2+x+1)) + O(x^100))

Formula

a(n) = a(n-1)+a(n-3)-a(n-4).

G.f.: x*(8*x^3+2*x^2+7*x+1) / ((x-1)^2*(x^2+x+1)).