1,2

Equals row sums of triangle A143119. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 26 2008

G.-H. Halphen, Sur les sommes des diviseurs des nombres entiers et les decompositions en deus carres, Bull. math. Soc. France, 6 (1877-1878), 119-.

P. A. MacMahon, Divisors of numbers and their continuations in the theory of partitions, Proc. London Math. Soc., (2) 19 (1919), 75-113; Coll. Papers II, pp. 303-341.

G. Chrystal, Algebra: An elementary text-book for the higher classes of secondary schools and for colleges, 6th ed, Chelsea Publishing Co., New York 1959 Part II, p. 346 Exercise XXI(18). MR0121327 (22 #12066)

A. P. Prudnikov, Yu. A. Brychkov and O.I. Marichev, "Integrals and Series", Volume 1: "Elementary Functions", Chapter 4: "Finite Sums", New York, Gordon and Breach Science Publishers, 1986-1992, Eqs. (5.1.29.3),(5.1.29.9)

T. D. Noe, Table of n, a(n) for n=1..10000

H. H. Chan and C. Krattenthaler, Recent progress in the study of representations of integers as sums of squares

Multiplicative with a(p^e) = p^e if p = 2; (p^(e+1)-1)/(p-1) if p > 2. - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.

a(n)=sigma(n)-sigma(n/2) for even n and =sigma(n) otherwise where sigma(n) is the sum of divisors of n (A000203). - Valery A. Liskovets (liskov(AT)im.bas-net.by), Apr 07 2002

G.f.: Sum_{n>=1} n*x^n/(1-x^(2*n)). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Oct 16 2002

Dirichlet g.f.: zeta(s)*zeta(s-1)*(1-1/2^s). - Michael Somos, Apr 05 2003

G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, u3, u6)=2*u1*u6 -u1*u3 -10*u2*u6 +u2^2 +2*u2*u3 +9*u6^2 - Michael Somos Apr 10 2005

G.f.: Sum_{k>0} x^(2k-1)/(1-x^(2k-1))^2. - Michael Somos Aug 17 2005

G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, u3, u6)=(u2-3*u6)^2-(u1-2*u2)*(u3-2*u6) - Michael Somos Sep 06 2005

G.f.: (1/8)theta_4''(0)/theta_4(0) = (Sum_{k>0} -(-1)^k k^2 q^(k^2))/(Sum_{k} (-1)^k q^(k^2)) where theta_4(u) is one of Jacobi's theta functions.

G.f.: Z'(0) K^2/(2Pi^2) = (K-E)K/(2Pi^2) where Z(u) is the Jacobi Zeta function and K, E are complete elliptic integrals. - Michael Somos Sep 06 2005

(PARI) a(n)=direuler(p=2, n, (1-(p<3)*X)/(1-X)/(1-p*X))[n]

(PARI) a(n)=if(n<1, 0, sumdiv(n, d, d/gcd(d, 2)))

A diagonal of A060047.

Cf. A000203.

Moebius transform is A026741. Cf. A000203.

Cf. A143119.

Adjacent sequences: A002128 A002129 A002130 this_sequence A002132 A002133 A002134

Sequence in context: A132118 A007843 A053196 this_sequence A063200 A063224 A023847

nonn,nice,easy,mult

njas, Simon Plouffe (plouffe(AT)math.uqam.ca)