A327164 Number of iterations of x -> gcd(usigma(x),x) needed to reach a fixed point, where usigma is the sum of unitary divisors of n (A034448).

0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 1, 3, 1, 2, 1, 3, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 3, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 2, 1, 0, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 0, 2, 2, 1, 2, 2, 3, 1, 2, 2, 3, 1, 1, 1, 2, 2

Offset

1,10

Links

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

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Prog

(PARI)
A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
A323166(n) = gcd(n, A034448(n));
A327164(n) = { my(u=A323166(n)); if(u==n, 0, 1+A327164(u)); }

Crossrefs

Cf. A034448, A323166, A327158 (positions of zeros).

Cf. also A326194.

Sequence in context: A243906 A100889 A206828 * A094781 A023582 A306717

Adjacent sequences: A327161 A327162 A327163 * A327165 A327166 A327167

Keyword

nonn

Author

Antti Karttunen, Aug 28 2019

Status

approved