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

1,2

Links

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

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

Mathematica

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

Prog

(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

Crossrefs

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

Cf. A000005, A051731, A114002.

Sequence in context: A243729 A200810 A365710 * A219792 A029622 A015126

Adjacent sequences: A114000 A114001 A114002 * A114004 A114005 A114006

Keyword

nonn

Author

Paul Barry, Nov 12 2005

Status

approved