A114003 Rows sums of triangle A114002.

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, 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, 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

Offset: 1

Author

Paul Barry, Nov 12 2005

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Also row sums of triangle A144515. - Gary W. Adamson, Nov 21 2007

Cf. A000005, A051731, A114002.

Programs

Mathematica

Table[2 DivisorSigma[0,n]-1,{n,97}] (* Stefano Spezia, Sep 08 2023 *)

PARI

N=66;x='x+O('x^N); /* that many terms */
Vec(sum(n=1,N,x^n*(1+x^n)/(1-x^n))) /* show terms */ /* Joerg Arndt, May 25 2011 */

PARI

A114003(n) = (2*numdiv(n))-1; \\ After Jovovic's formula. Antti Karttunen, May 25 2017

Formula

a(p) = 3, for primes p.

a(n) = 2*A000005(n) - 1. - Vladeta Jovovic, Sep 13 2006

Equals A051731 * [1, 2, 2, 2, ...]. - Gary W. Adamson, Sep 21 2007

G.f.: Sum_{n>0} x^n*(1+x^n)/(1-x^n). - Franklin T. Adams-Watters, Oct 09 2009