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

1,2

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).

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)).

Example

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

Mathematica

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

Prog

(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))

Crossrefs

Cf. A010888, A236652.

Sequence in context: A153382 A157911 A090097 * A257274 A022322 A302637

Adjacent sequences: A236650 A236651 A236652 * A236654 A236655 A236656

Keyword

nonn,base,easy

Author

Colin Barker, Jan 29 2014

Status

approved