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A114003 Rows sums of triangle A114002.

%I A114003 #33 Sep 08 2023 12:01:47
%S A114003 1,3,3,5,3,7,3,7,5,7,3,11,3,7,7,9,3,11,3,11,7,7,3,15,5,7,7,11,3,15,3,
%T A114003 11,7,7,7,17,3,7,7,15,3,15,3,11,11,7,3,19,5,11,7,11,3,15,7,15,7,7,3,
%U A114003 23,3,7,11,13,7,15,3,11,7,15,3,23,3,7,11,11,7,15,3,19,9,7,3,23,7,7,7,15,3,23,7,11,7,7,7,23,3
%N A114003 Rows sums of triangle A114002.
%H A114003 Antti Karttunen, <a href="/A114003/b114003.txt">Table of n, a(n) for n = 1..10000</a>
%F A114003 a(p) = 3, for primes p.
%F A114003 a(n) = 2*A000005(n) - 1. - _Vladeta Jovovic_, Sep 13 2006
%F A114003 Equals A051731 * [1, 2, 2, 2, ...]. - _Gary W. Adamson_, Sep 21 2007
%F A114003 G.f.: Sum_{n>0} x^n*(1+x^n)/(1-x^n). - _Franklin T. Adams-Watters_, Oct 09 2009
%t A114003 Table[2 DivisorSigma[0,n]-1,{n,97}] (* _Stefano Spezia_, Sep 08 2023 *)
%o A114003 (PARI) N=66;x='x+O('x^N); /* that many terms */
%o A114003 Vec(sum(n=1,N,x^n*(1+x^n)/(1-x^n))) /* show terms */ /* _Joerg Arndt_, May 25 2011 */
%o A114003 (PARI) A114003(n) = (2*numdiv(n))-1; \\ After Jovovic's formula. _Antti Karttunen_, May 25 2017
%Y A114003 Also row sums of triangle A144515. - _Gary W. Adamson_, Nov 21 2007
%Y A114003 Cf. A000005, A051731, A114002.
%K A114003 nonn
%O A114003 1,2
%A A114003 _Paul Barry_, Nov 12 2005