A382902 The largest cubefree divisor of the n-th biquadratefree number.

1, 2, 3, 4, 5, 6, 7, 4, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 12, 25, 26, 9, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 20, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 18, 55, 28, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 36

Offset

1,2

Links

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

Formula

a(n) = A007948(A046100(n)).

a(n) = (A382903(n) * A046100(n)^2)^(1/3).

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(4)^2 * Product_{p prime} (1 - 1/p^3 + 1/p^4 - 1/p^5) = 1.01974824991243823979... .

Mathematica

f[p_, e_] := p^Min[e, 2]; s[n_] := Module[{fct = FactorInteger[n]}, If[AllTrue[fct[[;; , 2]], # < 4 &], 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]) < 4, print1(prod(i = 1, #f~, f[i, 1]^min(f[i, 2], 2)), ", "))); }

Crossrefs

Cf. A046100, A007948, A013662.

Similar sequences: A382903, A382904, A382905, A382906.

Sequence in context: A355261 A353897 A366905 * A378759 A348262 A038389

Adjacent sequences: A382899 A382900 A382901 * A382903 A382904 A382905

Keyword

nonn,easy

Author

Amiram Eldar, Apr 08 2025

Status

approved