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

1,2

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

Links

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

Example

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.

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 &]]

Crossrefs

Cf. A000217, A000225, A007318.

Sequence in context: A027556 A195584 A225316 * A192708 A233531 A320303

Adjacent sequences: A272931 A272932 A272933 * A272935 A272936 A272937

Keyword

nonn

Author

Melvin Peralta, May 11 2016

Extensions

Mild editing. Wolfdieter Lang, May 31 2016

Status

approved