This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A106398 Binomial transform of denominators in a Zeta function. 0
 1, -1, -6, -19, -39, -66, -98, -129, -172, -330, -908, -2502, -5955, -12107 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The formula 1/Zeta(s) = 1 - 1/2^s - 1/3^s - 1/5^s + 1/6^s is shown on p. 249 of Derbyshire and relies upon strategies pioneered by Euler. REFERENCES John Derbyshire, "Prime Obsession, Bernhard Riemann and the Greatest Unsolved Problem in Mathematics", Joseph Henry Press, 2003, p. 249. LINKS FORMULA Given 1/Zeta(s) = 1 -1/2^s - 1/3^s - 1/5^s + 1/6^s - 1/7^s + 1/10^s - 1/11^s...; we apply the binomial transform to the terms: [1, -2, -3, -5, 6, -7, 10, -11, -13, 14, 15, -17, -19, 21...) which is the set of squarefree deficient numbers (A087246), along with the Mobius function of each term. EXAMPLE The terms 1, 2, 3, 5, 6, 7... = A087246, squarefree numbers. Applying the Mobius function rules to each of these, we get 1, -2, -3, -5, 6.... the Mobius function rules are: Given the domain N, the natural numbers 1,2,3..., Mu(1) = 1; Mu(n) of N = 0 if n has a square factor; Mu(n) = -1 if n is a prime or the product of an odd number of different primes; Mu(n) = 1 if n is the product of an even numbers of different primes. CROSSREFS Cf. A087246, A008683. Sequence in context: A031014 A010899 A090381 * A179986 A054567 A096957 Adjacent sequences:  A106395 A106396 A106397 * A106399 A106400 A106401 KEYWORD sign AUTHOR Gary W. Adamson, May 01 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .