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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<n} f(d) * f(n/d)) for n > 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<n, u[d]*u[n/d], 0)))/2); u};

v318657_18 = DirSqrt(vector(up_to, n, A087003(n)));

A318657(n) = numerator(v318657_18[n]);

A318658(n) = denominator(v318657_18[n]);

CROSSREFS

Cf. A005187, A087003, A318657 (numerators), A318659.

Sequence in context: A124333 A144757 A215136 * A318512 A295310 A002107

Adjacent sequences:  A318655 A318656 A318657 * A318659 A318660 A318661

KEYWORD

nonn,frac

AUTHOR

Antti Karttunen, Aug 31 2018

STATUS

approved

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