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A317926
Denominators of rational valued sequence whose Dirichlet convolution with itself yields Euler's phi (A000010).
5
1, 2, 1, 8, 1, 2, 1, 16, 2, 1, 1, 8, 1, 2, 1, 128, 1, 4, 1, 4, 1, 2, 1, 16, 1, 1, 2, 8, 1, 1, 1, 256, 1, 1, 1, 16, 1, 2, 1, 8, 1, 2, 1, 8, 1, 2, 1, 128, 2, 1, 1, 4, 1, 4, 1, 16, 1, 1, 1, 4, 1, 2, 2, 1024, 1, 2, 1, 1, 1, 1, 1, 32, 1, 1, 1, 8, 1, 1, 1, 64, 8, 1, 1, 8, 1, 2, 1, 16, 1, 2, 1, 8, 1, 2, 1, 256, 1, 4, 2, 1, 1, 1, 1, 8, 1
OFFSET
1,2
LINKS
FORMULA
a(n) = denominator of f(n), where f(1) = 1, f(n) = (1/2) * (A000010(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
MATHEMATICA
f[1] = 1; f[n_] := f[n] = (EulerPhi[n] - DivisorSum[n, f[#]*f[n/#] &, 1 < # < n &])/2; Denominator @ Array[f, 100] (* Amiram Eldar, Dec 12 2022 *)
PROG
(PARI)
A317925perA317926(n) = if(1==n, n, (eulerphi(n)-sumdiv(n, d, if((d>1)&&(d<n), A317925perA317926(d)*A317925perA317926(n/d), 0)))/2);
A317926(n) = denominator(A317925perA317926(n));
CROSSREFS
Cf. A000010, A317925 (numerators).
Cf. also A046644, A317832.
Sequence in context: A317928 A011327 A318454 * A318318 A318314 A230369
KEYWORD
nonn,frac
AUTHOR
Antti Karttunen, Aug 11 2018
STATUS
approved