A340087 a(n) = gcd(n-1, A091732(n)), where A091732 is an infinitary analog of Euler's phi function.

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

Offset: 1

Author

Antti Karttunen, Dec 31 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A091732, A340088, A340089.

Cf. also A049559.

Programs

PARI

ispow2(n) = (n && !bitand(n,n-1));
A302777(n) = ispow2(isprimepower(n));
A091732(n) = { my(m=1); while(n > 1, fordiv(n, d, if((dA302777(n/d), m *= ((n/d)-1); n = d; break))); (m); };
A340087(n) = gcd(n-1, A091732(n));

Formula

a(n) = gcd(n-1, A091732(n)).

a(n) = A091732(n) / A340088(n).

For n > 1, a(n) = (n-1) / A340089(n).