A113940 Triangular numbers that are also brilliant (A078972).

6, 10, 15, 21, 253, 703, 1081, 1711, 1891, 2701, 3403, 25651, 34453, 38503, 49141, 60031, 64261, 73153, 79003, 88831, 104653, 108811, 114481, 126253, 146611, 158203, 171991, 188191, 218791, 226801, 258121, 269011, 286903, 351541, 371953, 385003, 392941

Offset: 1

Author

Giovanni Resta, Jan 31 2006

Keywords

• base
• nonn

Comments

Smallest value where each factor has n digits for n = 1, 2, 3, 4, 5, are: 6 = 2 * 3; 253 = 11 * 23; 25651 = 113 * 227; 2035153 = 1009 * 2017; 202457503 = 10061 * 20123. [From Jonathan Vos Post, Apr 04 2009]

Examples

			253 = T(22) and 253 = 11*23 is brilliant.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A068443, A078972, A000217.

Programs

Mathematica

brilQ[n_]:=Module[{fin=FactorInteger[n]},Total[Transpose[fin][[2]]]==2&& Length[Union[IntegerLength[Transpose[fin][[1]]]]]==1]
Intersection[Accumulate[Range[850]],Select[Range[362000],brilQ]]  (* Harvey P. Dale, Feb 06 2011 *)

Formula

A000217 INTERSECTION A078972. Subset of A068443. [From Jonathan Vos Post, Apr 04 2009]