cp's OEIS Frontend

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

%I A272934 #27 Jul 04 2017 20:41:40
%S A272934 1,2,6,18,42,126,162,378,486,882,1458,2646,3078,3942,5418,9198,11826,
%T A272934 14406,16758,18522,24966,26406,37338,39366,42462,71442,77658,95922,
%U A272934 99078,113778,117306,143262,174762,175446,184842,265482,304038,308826,318402,351918
%N A272934 Depth of Pascal's triangle such that the number of elements in the triangle is a factor of the sum of the elements.
%C A272934 a(n) are the values m such that the expression (2^(m+1) - 2)/(m^2 + m) is an integer.
%C A272934 a(n) are the values m such that A000225(m)/A000217(m) is an integer.
%C A272934 It appears that a(n) == 2 (mod 4) for n > 1. - _Robert Israel_, Jul 04 2017
%H A272934 Robert Israel, <a href="/A272934/b272934.txt">Table of n, a(n) for n = 1..300</a> (first 66 terms from Melvin Peralta)
%e A272934 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.
%e A272934 6 is a term because A000225(6)/A000217(6) = 63/21 = 3, an integer.
%p A272934 select(t -> 2 &^ t  - 1 mod t*(t+1)/2 = 0, [$1..10^6]); # _Robert Israel_, Jul 04 2017
%t A272934 Join[{1}, Select[Range[10^6], PowerMod[2, #+1, #^2+#] == 2 &]]
%Y A272934 Cf. A000217, A000225, A007318.
%K A272934 nonn
%O A272934 1,2
%A A272934 _Melvin Peralta_, May 11 2016
%E A272934 Mild editing. _Wolfdieter Lang_, May 31 2016