A272934 Depth of Pascal's triangle such that the number of elements in the triangle is a factor of the sum of the elements.

1, 2, 6, 18, 42, 126, 162, 378, 486, 882, 1458, 2646, 3078, 3942, 5418, 9198, 11826, 14406, 16758, 18522, 24966, 26406, 37338, 39366, 42462, 71442, 77658, 95922, 99078, 113778, 117306, 143262, 174762, 175446, 184842, 265482, 304038, 308826, 318402, 351918

Offset: 1

Author

Melvin Peralta, May 11 2016

Keywords

• nonn

Comments

a(n) are the values m such that the expression (2^(m+1) - 2)/(m^2 + m) is an integer.

a(n) are the values m such that A000225(m)/A000217(m) is an integer.

It appears that a(n) == 2 (mod 4) for n > 1. - Robert Israel, Jul 04 2017

Examples

			a(2) = 6 because if Pascal's triangle is written out to 6 rows, there will be 21 elements whose sum is 63, and 21 is a factor of 63.
6 is a term because A000225(6)/A000217(6) = 63/21 = 3, an integer.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..300 (first 66 terms from Melvin Peralta)

Crossrefs

Cf. A000217, A000225, A007318.

Programs

Maple

select(t -> 2 &^ t  - 1 mod t*(t+1)/2 = 0, [$1..10^6]); # Robert Israel, Jul 04 2017

Mathematica

Join[{1}, Select[Range[10^6], PowerMod[2, #+1, #^2+#] == 2 &]]

Extensions

Mild editing. Wolfdieter Lang, May 31 2016