A340089 a(n) = (n-1) / gcd(n-1, A091732(n)), where A091732 is an infinitary analog of Euler's phi function.

0, 1, 1, 1, 1, 5, 1, 7, 1, 9, 1, 11, 1, 13, 7, 1, 1, 17, 1, 19, 5, 21, 1, 23, 1, 25, 13, 3, 1, 29, 1, 31, 8, 33, 17, 35, 1, 37, 19, 13, 1, 41, 1, 43, 11, 45, 1, 47, 1, 49, 25, 17, 1, 53, 27, 55, 14, 57, 1, 59, 1, 61, 31, 7, 4, 13, 1, 67, 17, 23, 1, 71, 1, 73, 37, 25, 19, 77, 1, 79, 1, 81, 1, 83, 21, 85, 43, 29, 1, 89

Offset

1,6

Links

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

Formula

a(n) = (n-1) / A340087(n) = (n-1) / gcd(n-1, A091732(n)).

Prog

(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((d<n)&&A302777(n/d), m *= ((n/d)-1); n = d; break))); (m); };
A340089(n) = ((n-1)/gcd(n-1, A091732(n)));

Crossrefs

Cf. A091732, A340087, A340088.

Cf. also A160596.

Sequence in context: A353574 A265293 A348502 * A089027 A354432 A023890

Adjacent sequences: A340086 A340087 A340088 * A340090 A340091 A340092

Keyword

nonn

Author

Antti Karttunen, Dec 31 2020

Status

approved