A382888 The squarefree kernel of the n-th cubefree number.

1, 2, 3, 2, 5, 6, 7, 3, 10, 11, 6, 13, 14, 15, 17, 6, 19, 10, 21, 22, 23, 5, 26, 14, 29, 30, 31, 33, 34, 35, 6, 37, 38, 39, 41, 42, 43, 22, 15, 46, 47, 7, 10, 51, 26, 53, 55, 57, 58, 59, 30, 61, 62, 21, 65, 66, 67, 34, 69, 70, 71, 73, 74, 15, 38, 77, 78, 79, 82

Offset

1,2

Links

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

Formula

a(n) = A007947(A004709(n)).

a(n) = A004709(n)/sqrt(A382889(n)) = A004709(n)/A382890(n).

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

a(A371188(n)) = A005117(n).

Sum_{k=1..n} a(k) ~ c * n^2 / 2. where c = zeta(3)^2 * Product_{p prime} (1 - 1/p^2 + 1/p^3 - 1/p^4) = 0.98875409459226057523... .

Mathematica

s[n_] := Module[{f = FactorInteger[n]}, If[AllTrue[f[[;; , 2]], # < 3 &], Times @@ f[[;; , 1]], 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(vecprod(f[, 1]), ", "))); }

Crossrefs

Cf. A002117, A004709, A005117, A007947, A371188.

Similar sequences: A382889, A382890, A382891.

Sequence in context: A287620 A304491 A381614 * A277803 A062789 A375240

Adjacent sequences: A382885 A382886 A382887 * A382889 A382890 A382891

Keyword

nonn,easy

Author

Amiram Eldar, Apr 07 2025

Status

approved