The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A217334 G.f.: exp( Sum_{n>=1} (2*sigma(n^2) - sigma(n)^2 - sigma(n,2))/2 * x^n/n ). 1
1, 0, 0, 0, -1, 0, -1, 0, -3, -1, 0, 0, -4, 1, 3, 0, 4, 3, 1, 1, 16, 4, 10, 0, 15, -4, 6, 0, 14, -15, -11, -9, -29, -5, -56, -14, -56, -24, -101, 10, -140, -8, -25, 18, -101, 27, 7, 50, 91, 128, 222, 29, 300, 207, 516, 119, 614, 73, 762, 115, 510, 89, 614, -280 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,9
COMMENTS
The number of contiguous signs appear to increase (roughly) in proportion to the square-root of the number of terms.
LINKS
EXAMPLE
G.f.: A(x) = 1 - x^4 - x^6 - 3*x^8 - x^9 - 4*x^12 + x^13 + 3*x^14 + 4*x^16 +...
where
log(A(x)) = -4*x^4/4 - 6*x^6/6 - 28*x^8/8 - 9*x^9/9 - 10*x^10/10 - 94*x^12/12 - 14*x^14/14 - 15*x^15/15 - 140*x^16/16 +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, (sigma(m^2)-sigma(m)^2/2-sigma(m, 2)/2)*x^m/m)+x*O(x^n)), n)}
for(n=0, 70, print1(a(n), ", "))
CROSSREFS
Sequence in context: A059202 A244963 A144452 * A369455 A353859 A058865
KEYWORD
sign
AUTHOR
Paul D. Hanna, Sep 30 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 20 08:05 EDT 2024. Contains 372703 sequences. (Running on oeis4.)