A396068 Product of squarefree divisors of n that are <= sqrt(n).

1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 5, 2, 3, 2, 1, 30, 1, 2, 3, 2, 5, 36, 1, 2, 3, 10, 1, 36, 1, 2, 15, 2, 1, 36, 7, 10, 3, 2, 1, 36, 5, 14, 3, 2, 1, 180, 1, 2, 21, 2, 5, 36, 1, 2, 3, 70, 1, 36, 1, 2, 15, 2, 7, 36, 1, 10, 3, 2, 1, 252, 5

Offset

1,4

Links

Table of n, a(n) for n=1..85.

Mathematica

a[n_] := Times @@ Select[Divisors[n], SquareFreeQ[#] && # <= Sqrt[n] &]; Array[a, 85]

Prog

(PARI) a(n) = vecprod(select(x->(x<=sqrt(n) && issquarefree(x)), divisors(n))); \\ Michel Marcus, May 15 2026
(Python)
from math import isqrt, prod
from itertools import combinations
from sympy import primefactors
def A396068(n):
    c, ps, m = 1, primefactors(n), isqrt(n)
    for l in range(1, len(ps)+1):
        for p in combinations(ps, l):
            if (q:=prod(p)) <= m:
                c *= q
    return c # Chai Wah Wu, May 20 2026

Crossrefs

Cf. A007955, A072499, A078599, A333752, A382486, A396067.

Sequence in context: A338669 A219254 A382486 * A372833 A072504 A072499

Adjacent sequences: A396065 A396066 A396067 * A396069 A396070 A396072

Keyword

nonn,easy

Author

Ilya Gutkovskiy, May 15 2026

Status

approved