A113502 A number n is included if at least one of its divisors > 1 is a triangular number (i.e., is of the form m(m+1)/2, m >= 2).

3, 6, 9, 10, 12, 15, 18, 20, 21, 24, 27, 28, 30, 33, 36, 39, 40, 42, 45, 48, 50, 51, 54, 55, 56, 57, 60, 63, 66, 69, 70, 72, 75, 78, 80, 81, 84, 87, 90, 91, 93, 96, 99, 100, 102, 105, 108, 110, 111, 112, 114, 117, 120, 123, 126, 129, 130, 132, 135, 136, 138, 140, 141

Offset: 1

Author

Leroy Quet, Jan 10 2006

Keywords

• nonn

Comments

A number n is in the sequence iff it is not a "triangle-free" positive integer.

Multiples of A226863. - Charles R Greathouse IV, Jul 29 2016

Examples

			12 is included because its divisors are 1, 2, 3, 4, 6 and 12, two of which (3 and 6) are triangular numbers > 1.
		

Links

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

Crossrefs

Cf. A112886, A000217, A013929, A226863.

Programs

Mathematica

v={};Do[If[b=Select[Divisors[n], #>1 && IntegerQ[(1+8#)^(1/2)]&]; b!={}, AppendTo[v, n]], {n, 200}]; v (* Farideh Firoozbakht, Jan 12 2006 *)
Select[Range[200],AnyTrue[Rest[Divisors[#]],OddQ[Sqrt[8#+1]]&]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 13 2017 *)

PARI

is(n)=fordiv(n,d, if(ispolygonal(d,3) && d>1, return(1))); 0 \\ Charles R Greathouse IV, Jul 29 2016

Formula

a(n) = A088723(n)/2. - Ray Chandler, May 29 2008

Extensions

More terms from Farideh Firoozbakht, Jan 12 2006