A374200 a(n) is the minimum value of A347381 that it obtains among the unitary divisors of n larger than 1, where A347381 is the distance from n to the nearest common ancestor of n and sigma(n) in the Doudna-tree (A005940). By convention a(1) = 0.

0, 0, 1, 1, 1, 0, 3, 2, 2, 0, 3, 1, 2, 0, 1, 3, 6, 0, 5, 1, 1, 0, 7, 1, 3, 0, 3, 0, 8, 0, 10, 4, 1, 0, 1, 1, 4, 0, 1, 1, 10, 0, 9, 1, 1, 0, 13, 1, 4, 0, 1, 1, 15, 0, 1, 2, 1, 0, 15, 1, 7, 0, 2, 5, 1, 0, 12, 1, 1, 0, 19, 2, 9, 0, 1, 1, 3, 0, 19, 1, 3, 0, 20, 0, 1, 0, 1, 2, 22, 0, 2, 1, 1, 0, 1, 1, 24, 0, 2, 1, 20

Offset

1,7

Comments

In contrast to A374204 and A374214 it seems that this sequence has no missing values, i.e., it is probably surjective on N.

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for sequences related to sigma(n)

Formula

a(1) = 0, and for n > 1, a(n) = Min_{d|n, d>1, gcd(d,n/d)=1} A347381(d).

Prog

(PARI) A374200(n) = { my(m=-1, x); fordiv(n, d, if(d>1 && 1==gcd(d, n/d), x = A347381(d); if(m<0 || x<m, m=x))); if(-1==m, 0, m); };

Crossrefs

Cf. A005940, A347381, A347383.

Cf. also A374204, A374214.

Sequence in context: A178609 A144948 A108335 * A239474 A326152 A308181

Adjacent sequences: A374197 A374198 A374199 * A374201 A374202 A374203

Keyword

nonn

Author

Antti Karttunen, Jul 09 2024

Status

approved