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 A318658 Denominators of the sequence whose Dirichlet convolution with itself yields A087003, a(2n) = 0 and a(2n+1) = moebius(2n+1). 5
 1, 1, 2, 1, 2, 1, 2, 1, 8, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 8, 1, 16, 1, 2, 1, 2, 1, 4, 1, 4, 1, 2, 1, 4, 1, 2, 1, 2, 1, 16, 1, 2, 1, 8, 1, 4, 1, 2, 1, 4, 1, 4, 1, 2, 1, 2, 1, 16, 1, 4, 1, 2, 1, 4, 1, 2, 1, 2, 1, 16, 1, 4, 1, 2, 1, 128, 1, 2, 1, 4, 1, 4, 1, 2, 1, 4, 1, 4, 1, 4, 1, 2, 1, 16, 1, 2, 1, 2, 1, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The sequence seems to give the denominators of several other similarly constructed "Dirichlet Square Roots". LINKS Antti Karttunen, Table of n, a(n) for n = 1..16384 FORMULA a(n) = denominator of f(n), where f(1) = 1, f(n) = (1/2) * (A087003(n) - Sum_{d|n, d>1, d 1. a(n) = 2^A318659(n). a(2n) = 1, a(2n-1) = A046644(2n-1) = A318512(2n-1), for all n >= 1. PROG (PARI) up_to = 65537; A087003(n) = ((n%2)*moebius(n)); \\ I.e. a(n) = A000035(n)*A008683(n). DirSqrt(v) = {my(n=#v, u=vector(n)); u[1]=1; for(n=2, n, u[n]=(v[n]/v[1] - sumdiv(n, d, if(d>1&&d

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Last modified December 18 23:46 EST 2018. Contains 318245 sequences. (Running on oeis4.)