A319676 Numerator of A047994(n)/n where A047994 is the unitary totient function.

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

Links

Table of n, a(n) for n=1..75.

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).

Cf. A002110, A038110, A006093.

Sequence in context: A345937 A105587 A345998 * A049073 A076388 A354988

Adjacent sequences: A319673 A319674 A319675 * A319677 A319678 A319679

Keyword

nonn,frac

Author

Michel Marcus, Sep 26 2018

Status

approved