A396771 Second least non-divisor of n.

3, 4, 4, 5, 3, 5, 3, 5, 4, 4, 3, 7, 3, 4, 4, 5, 3, 5, 3, 6, 4, 4, 3, 7, 3, 4, 4, 5, 3, 7, 3, 5, 4, 4, 3, 7, 3, 4, 4, 6, 3, 5, 3, 5, 4, 4, 3, 7, 3, 4, 4, 5, 3, 5, 3, 5, 4, 4, 3, 8, 3, 4, 4, 5, 3, 5, 3, 5, 4, 4, 3, 7, 3, 4, 4, 5, 3, 5, 3, 6, 4, 4, 3, 8, 3, 4, 4, 5, 3, 7, 3, 5, 4

Offset

1,1

Comments

An integer m >= 3 appears in the sequence if and only if m is a prime power or twice a prime power.

Links

David Radcliffe, Table of n, a(n) for n = 1..10000

Bakir Farhi, On the average asymptotic behavior of a certain type of sequences of integers, Integers 9 (2009), 555-567.

Formula

Sum_{n=1..N} a(n) = c*N + O((log N)^2 / (log log N)), where

c = Sum_{m >= 0} (1 + Sum_{m/2 < p^a <= m} (p-1)) / lcm(1,2,...,m) ~ 4.287434141625.

Mathematica

f[n_, q_ : 1] := Module[{c, k}, c = 0; k = 2; While[If[! Divisible[n, k], c++]; c < q, k++]; k]; Table[f[n, 2], {n, 120}] (* Michael De Vlieger, Jun 08 2026 *)

Prog

(Python)
from itertools import count, islice
def A396771(n: int, rank: int = 2) -> int:
    assert n > 0 and rank > 0, "Arguments must be positive integers."
    return next(islice(filter(lambda x: n % x, count(2)), rank - 1, rank))
(PARI) a(n) = my(nb=0, i=1); while(nb !=2, i++; if (n % i, nb++)); i; \\ Michel Marcus, Jun 08 2026

Crossrefs

Cf. A007978, A140485.

Sequence in context: A158012 A334961 A032446 * A271563 A342938 A028949

Adjacent sequences: A396767 A396768 A396770 * A396772 A396776 A396777

Keyword

nonn,easy

Author

David Radcliffe, Jun 04 2026

Status

approved