This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A126690 Multiplicative function defined for prime powers by a(p^k) = p + p^2 + p^3 + ... + p^(k-1) - 1 (k >= 1). 2
 1, -1, -1, 1, -1, 1, -1, 5, 2, 1, -1, -1, -1, 1, 1, 13, -1, -2, -1, -1, 1, 1, -1, -5, 4, 1, 11, -1, -1, -1, -1, 29, 1, 1, 1, 2, -1, 1, 1, -5, -1, -1, -1, -1, -2, 1, -1, -13, 6, -4, 1, -1, -1, -11, 1, -5, 1, 1, -1, 1, -1, 1, -2, 61, 1, -1, -1, -1, 1, -1, -1, 10, -1, 1, -4, -1, 1, -1, -1, -13, 38, 1, -1, 1, 1, 1, 1, -5, -1, 2, 1, -1, 1, 1, 1, -29, -1, -6, -2, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS If we change the definition to a(p^k) = p + p^2 + p^3 + ... + p^k - 1 (k >= 1) we get (-1)sigma(n), A046090. LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 EXAMPLE a(5) = -1, a(9) = 3-1 = 2, a(45) = (-1)*2 = -2. MAPLE pksum := proc(L) local p, k ; p := op(1, L) ; k := op(2, L) ; (p^k-p)/(p-1)-1 ; end: A126690 := proc(n) local pe, a ; if n = 1 then RETURN(1) ; else a := 1 ; pe := ifactors(n)[2] ; for d in pe do a := a*pksum(d) ; od: RETURN(a) ; fi; end: for n from 1 to 120 do printf("%d, ", A126690(n)) ; od: # R. J. Mathar, Aug 08 2008 PROG (Scheme, with memoization-macro definec) (definec (A126690 n) (cond ((= 1 n) n) ((= 1 (A067029 n)) (- (A126690 (A028234 n)))) (else (* (+ -1 (add (lambda (k) (expt (A020639 n) k)) 1 (- (A067029 n) 1))) (A126690 (A028234 n)))))) ;; Auxiliary function add implements sum_{i=lowlim..uplim} intfun(i) (define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i))))))) ;; Antti Karttunen, Sep 23 2017 CROSSREFS Sequence in context: A326327 A113103 A033325 * A263007 A104714 A085119 Adjacent sequences:  A126687 A126688 A126689 * A126691 A126692 A126693 KEYWORD sign,mult AUTHOR N. J. A. Sloane, Feb 14 2008, based on a posting to the Sequence Fans Mailing List by Yasutoshi Kohmoto, Feb 02 2005 EXTENSIONS Extended beyond a(30) by R. J. Mathar, Aug 08 2008 More terms from Antti Karttunen, Sep 23 2017 STATUS approved

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

Last modified October 14 15:03 EDT 2019. Contains 328019 sequences. (Running on oeis4.)