A382890 The square root of the largest square dividing the n-th cubefree number.

1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 5, 1, 2, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 7, 5, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 5, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 7, 3, 10, 1, 1

Offset

1,4

Comments

The product of the non-unitary prime divisors of the n-th cubefree number.

Also, the square root of the powerful part of the n-th cubefree number.

All the terms are squarefree.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000188(A004709(n)).

a(n) = sqrt(A382889(n)).

a(n) = A004709(n)/A382888(n).

a(n) = sqrt(A004709(n)/A382891(n)).

a(A371188(n)) = 1.

Mathematica

f[p_, e_] := p^If[e == 1, 0, 1]; s[n_] := Module[{fct = FactorInteger[n]}, If[AllTrue[fct[[;; , 2]], # < 3 &], Times @@ f @@@ fct, Nothing]]; Array[s, 100]

Prog

(PARI) list(lim) = {my(f); print1(1, ", "); for(k = 2, lim, f = factor(k); if(vecmax(f[, 2]) < 3, print1(prod(i = 1, #f~, f[i, 1]^if(f[i, 2] == 1, 0, 1)), ", "))); }

Crossrefs

Cf. A000188, A004709, A005117, A057521, A371188 (positions of 1's).

Similar sequences: A382888, A382889, A382891.

Sequence in context: A318812 A337066 A324247 * A138904 A357138 A357180

Adjacent sequences: A382887 A382888 A382889 * A382891 A382892 A382893

Keyword

nonn,easy

Author

Amiram Eldar, Apr 07 2025

Status

approved