OFFSET
1,4
COMMENTS
b(n) = A046643(n)/A046644(n) is multiplicative with b(p^n) = (2n-1)!!/2^n/n!. Dirichlet g.f. of A046643(n)/A046644(n) is sqrt(zeta(x)). - Christian G. Bower, May 16 2005
LINKS
FORMULA
EXAMPLE
b_1, b_2, ... = 1, 1/2, 1/2, 3/8, 1/2, 1/4, 1/2, 5/16, 3/8, 1/4, 1/2, 3/16, ...
MAPLE
b := proc(n) option remember; local c, i, t1; if n = 1 then 1 else c := 1; t1 := divisors(n);
for i from 2 to nops(t1)-1 do c := c-b(t1[ i ])*b(n/t1[ i ]); od; c/2; fi; end;
MATHEMATICA
b[1] = 1; b[n_] := b[n] = (dn = Divisors[n]; c = 1;
Do[c = c - b[dn[[i]]]*b[n/dn[[i]]], {i, 2, Length[dn] - 1}]; c/2); a[n_] := Numerator[b[n]]; a /@ Range[90] (* Jean-François Alcover, Apr 04 2011, after Maple version *)
PROG
(PARI)
A046643perA046644(n) = { my(c=1); if(1==n, c, fordiv(n, d, if((d>1)&&(d<n), c -= (A046643perA046644(d)*A046643perA046644(n/d)))); (c/2)); }
A046643(n) = numerator(A046643perA046644(n)); \\ After Maple-program, Antti Karttunen, Jul 08 2017
(Scheme)
;; Or, after Christian G. Bower's May 16 2005 comment:
(definec (A046643perA046644 n) (if (= 1 n) n (* (/ (A010050 (A067029 n)) (A000290 (A000165 (A067029 n)))) (A046643perA046644 (A028234 n)))))
(define (A046643 n) (numerator (A046643perA046644 n)))
(define (A046644 n) (denominator (A046643perA046644 n)))
;; Antti Karttunen, Jul 08 2017
CROSSREFS
KEYWORD
nonn,easy,frac,nice,mult
AUTHOR
N. J. A. Sloane, Dec 11 1999
STATUS
approved