A345937 a(n) = gcd(n-1, uphi(n)), where uphi is unitary totient (or unitary phi) function, A047994.

1, 1, 2, 3, 4, 1, 6, 7, 8, 1, 10, 1, 12, 1, 2, 15, 16, 1, 18, 1, 4, 1, 22, 1, 24, 1, 26, 9, 28, 1, 30, 31, 4, 1, 2, 1, 36, 1, 2, 1, 40, 1, 42, 1, 4, 1, 46, 1, 48, 1, 2, 3, 52, 1, 2, 1, 4, 1, 58, 1, 60, 1, 2, 63, 16, 5, 66, 1, 4, 3, 70, 1, 72, 1, 2, 3, 4, 1, 78, 1, 80, 1, 82, 1, 4, 1, 2, 1, 88, 1, 18, 1, 4, 1, 2, 1, 96

Offset: 1

Author

Antti Karttunen, Jun 29 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A047994, A345938, A345939.

Cf. also A049559, A340087, A323409, A345947.

Programs

PARI

A047994(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^f[2, i])-1); };
A345937(n) = gcd(n-1, A047994(n));

Formula

a(n) = gcd(n-1, A047994(n)).

a(n) = A047994(n) / A345938(n).

a(n) = (n-1) / A345939(n), for n > 1.

a(2n-1) = A345947(2n-1), for n >= 1.