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 A046643 From square root of Riemann zeta function: form Dirichlet series Sum b_n/n^s whose square is zeta function; sequence gives numerator of b_n. 23
 1, 1, 1, 3, 1, 1, 1, 5, 3, 1, 1, 3, 1, 1, 1, 35, 1, 3, 1, 3, 1, 1, 1, 5, 3, 1, 5, 3, 1, 1, 1, 63, 1, 1, 1, 9, 1, 1, 1, 5, 1, 1, 1, 3, 3, 1, 1, 35, 3, 3, 1, 3, 1, 5, 1, 5, 1, 1, 1, 3, 1, 1, 3, 231, 1, 1, 1, 3, 1, 1, 1, 15, 1, 1, 3, 3, 1, 1, 1, 35, 35, 1, 1, 3, 1, 1, 1, 5, 1, 3 (list; graph; refs; listen; history; text; internal format)
 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 That is, b(p^n) = A001147(n) / (A000079(n)*A000142(n)) = A010050(n)/A000290(A000165(n)) = (2n)!/((2^n*n!)^2). - Antti Karttunen, Jul 08 2017 LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 FORMULA Sum_{b|d} b(d)b(n/d) = 1. Also b_{2^j} = A001790[ j ]/2^A005187[ j ]. From Antti Karttunen, Jul 08 2017: (Start) Multiplicative with a(p^n) = A001790(n). a(1) = 1; for n > 1, a(n) = A001790(A067029(n)) * a(A028234(n)). (End) 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

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Last modified February 17 17:52 EST 2019. Contains 320222 sequences. (Running on oeis4.)