A389105 a(n) is the smallest value of k such that gcd(A381466(k-1), k) = n.

1, 4, 27, 8, 35, 30, 847, 56, 99, 250, 209, 252, 2587, 1764, 75, 48, 1037, 328239090, 58159

Offset

1,2

Comments

Equivalently, a(n) is the first time n is a divisor at a division step of A381466; i.e., a(n) = the smallest value of k such that k/A381466(k) = n.

We conjecture that a(n) > 0 for all n; i.e., every positive integer is a divisor in A381466 at least once; indeed, we conjecture that every positive integer is a divisor infinitely many times. For positive values found so far, a(n) > 1.2^(n-1), and we also conjecture this is always true.

In the first 10^12 terms of A381466:

- there are 55 known terms up to a(106), see linked a-file;

- the smallest number that has not yet appeared as a divisor is 20;

- 106 is the largest unique divisor to appear at index 2028511506;

- 73 is the last number to appear as a new divisor at index 160322038411.

Links

Table of n, a(n) for n=1..19.

Sam Chapman, Table of n, a(n) for all terms < 10^12 (where ? denotes missing, larger values)

Example

a(2) = 4 because step 4 is the first time we divide by 2 in A381466.
a(3) = 27 because step 27 is the first time we divide by 3 in A381466.

Prog

(PARI) a(n) = my(k=1, v=4, g); while ((g=gcd(k, v)) != n, k++; if (g==1, v += k-1, v = (k-1)/g)); k; \\ Michel Marcus, May 17 2026

Crossrefs

Cf. A381466.

Sequence in context: A351366 A365636 A345311 * A125723 A094543 A136511

Adjacent sequences: A389102 A389103 A389104 * A389106 A389107 A389108

Keyword

nonn,more

Author

Sam Chapman, Mar 11 2026

Status

approved