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A319676
Numerator of A047994(n)/n where A047994 is the unitary totient function.
2
1, 1, 2, 3, 4, 1, 6, 7, 8, 2, 10, 1, 12, 3, 8, 15, 16, 4, 18, 3, 4, 5, 22, 7, 24, 6, 26, 9, 28, 4, 30, 31, 20, 8, 24, 2, 36, 9, 8, 7, 40, 2, 42, 15, 32, 11, 46, 5, 48, 12, 32, 9, 52, 13, 8, 3, 12, 14, 58, 2, 60, 15, 16, 63, 48, 10, 66, 12, 44, 12, 70, 7, 72, 18, 16
OFFSET
1,3
FORMULA
a(p) = p-1, for p prime (see A006093).
a(A002110(n)) = A038110(n).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A319677(k) = Product_{p prime} (1 - 1/(p*(p+1))) = 0.7044422... (A065463). - Amiram Eldar, Nov 21 2022
MATHEMATICA
uphi[n_] := Product[{p, e} = pe; p^e - 1, {pe, FactorInteger[n]}];
a[n_] := If[n == 1, 1, Numerator[uphi[n]/n]];
Array[a, 100] (* Jean-François Alcover, Jan 10 2022 *)
PROG
(PARI) a(n)=my(f=factor(n)~); numerator(prod(i=1, #f, f[1, i]^f[2, i]-1)/n);
CROSSREFS
Cf. A047994, A030163, A065463, A305678, A319481, A319677 (denominators).
Sequence in context: A345937 A105587 A345998 * A049073 A076388 A354988
KEYWORD
nonn,frac
AUTHOR
Michel Marcus, Sep 26 2018
STATUS
approved