1,3

a(2*n) = A054785(2*n) - A000203(n). - from Reinhard Zumkeller (reinhard.zumkeller@gmail.com), Apr 23 2008

Aicardi Francesca, MATRICIAL FORMULAE FOR PARTITIONS, arXiv:0806.1273.

F. Hirzebruch et al., Manifolds and Modular Forms, Vieweg 1994 p 133.

J. Riordan, Combinatorial Identities, Wiley, 1968, p. 187.

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

M. Baake and R. V. Moody, Similarity submodules and root systems in four dimensions, Canad. J. Math. 51 (1999), 1258-1276.

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for "core" sequences

Inverse Moebius Transform of [0, 1, 0, 3, 0, 5, ...]

Dirichlet g.f.: zeta(s)*zeta(s-1)*(1-2^(1-s)).

a(2n)=A000203(2n)-2*A000203(n), a(2n+1)=A000203(2n+1) - Henry Bottomley (se16(AT)btinternet.com), May 16 2000

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

a(n) = Sum_{d divides n} (-1)^(d+1)*n/d. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 06 2002

Sum(k=1, n, a(k)) is asymptotic to c*n^2 where c=Pi^2/24. - Benoit Cloitre, Dec 29, 2002

G.f.: Sum_{n>0} nx^n/(1+x^n). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Oct 11 2002

G.f.: (theta_3(q)^4 + theta_2(q)^4 -1)/24.

G.f.: Sum_{k>0} -(-x)^k/(1-x^k)^2. - Michael Somos Oct 29 2005

a(n)=A050449(n)+A050452(n); a(A000079(n))=1; a(A005408(n))=A000203(A005408(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Apr 18 2006

Dirichlet g.f.: zeta(s)*zeta(s-1)*(1-2^(1-s)). - Ralf Stephan, Jun 17 2007

A000593 := proc(n) local d, s; s := 0; for d from 1 by 2 to n do if n mod d = 0 then s := s+d; fi; od; RETURN(s); end;

Table[a := Select[Divisors[n], OddQ[ # ]&]; Sum[a[[i]], {i, 1, Length[a]}], {n, 1, 60}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 01 2006

(PARI) a(n)=if(n<1, 0, sumdiv(n, d, (-1)^(d+1)*n/d))

(PARI from Joerg Arndt (arndt(AT)jjj.de), May 03, 2008)

N=17; default(seriesprecision, N); x=z+O(z^(N+1))

c=sum(j=1, N, j*x^j); \\ log case

s=-log(prod(j=1, N, (1+x^j)^(1))); \\ A000593 Sum of odd divisors of n.

s=serconvol(s, c)

v=Vec(s)

Cf. A000005, A000203, A001227, A050999-A051002, A078471.

Sequence in context: A127555 A117001 A098986 this_sequence A115607 A076717 A120422

Adjacent sequences: A000590 A000591 A000592 this_sequence A000594 A000595 A000596

nonn,core,easy,nice,mult

njas