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!)
A123707 a(n) = Sum_{k=1..n} A123706(n,k)*2^(k-1). 5
1, 0, 1, 3, 7, 14, 31, 60, 126, 248, 511, 1005, 2047, 4064, 8183, 16320, 32767, 65394, 131071, 261885, 524255, 1048064, 2097151, 4193220, 8388600, 16775168, 33554304, 67104765, 134217727, 268427002, 536870911, 1073725440, 2147483135 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
Triangle A123706 is the matrix inverse of triangle A010766(n,k) = [n/k].
LINKS
FORMULA
G.f.: Sum_{k>=1} mu(k) * x^k * (1 - x^k) / (1 - 2*x^k). - Ilya Gutkovskiy, Feb 06 2020
MATHEMATICA
t[n_, k_] := If[Divisible[n, k], MoebiusMu[n/k], 0] - If[Divisible[n, k + 1], MoebiusMu[n/(k + 1)], 0]; Table[Sum[t[n, k]*2^(k - 1), {k, 1, n}], {n, 1, 50}] (* G. C. Greubel, Oct 26 2017 *)
PROG
(PARI) {a(n)=sum(k=1, n, (matrix(n, n, r, c, if(r>=c, floor(r/c)))^-1)[n, k]*2^(k-1))}
CROSSREFS
Sequence in context: A139817 A173010 A036892 * A011947 A129629 A354463
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 09 2006
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 March 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)