%I #22 Apr 16 2012 14:09:51
%S 1,2,3,2,2,-5,2,3,7,2,2,2,3,3,2,-5,11,2,2,3,-13,2,7,3,-5,2,2,2,2,-17,
%T 2,3,3,19,2,2,-5,3,7,2,11,23,2,2,2,3,-5,-5,2,-13,3,3,3,2,2,7,-29,2,3,
%U -5,31,2,2,2,2,2,3,11,2,-17,-5,7,2,2,3,3,-37
%N Triangle read by rows in which row n lists the prime factors of n with repetition, with a(1) = 1, but with the primes of the form 4k + 1 multiplied by -1.
%C The row products of triangle give A209662. Also the row products of triangle divided by n give A209661. The mentioned sequences are related to an infinite series which is equal to pi, due to Leonhard Euler.
%e Written as a triangle begins:
%e 1;
%e 2;
%e 3;
%e 2, 2;
%e -5;
%e 2, 3;
%e 7;
%e 2, 2, 2;
%e 3, 3;
%e 2, -5;
%e 11;
%e 2, 2, 3;
%e -13;
%e 2, 7;
%e 3, -5;
%e 2, 2, 2, 2;
%Y Absolute values give A027746.
%Y Cf. A002144, A002145, A209661, A209662.
%K sign,tabf
%O 1,2
%A _Omar E. Pol_, Apr 15 2012
|