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

Author

Antti Karttunen, Jul 09 2024

Keywords

• nonn

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)

Crossrefs

Cf. A005940, A347381, A347383.

Cf. also A374204, A374214.

Programs

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
				

Formula

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