A382903 The largest cubefree unitary divisor of the n-th biquadratefree number.

1, 2, 3, 4, 5, 6, 7, 1, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 3, 25, 26, 1, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 5, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 2, 55, 7, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 9, 73

Offset

1,2

Links

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

Formula

a(n) = A360539(A046100(n)).

a(n) = A382902(n)^3 / A046100(n)^2.

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(4)^2 * Product_{p prime} (1 - 1/p^3 + 1/p^6 - 1/p^7) = 0.98420942697128846925... .

Mathematica

f[p_, e_] := p^If[e < 3, e, 0]; 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]^if(f[i, 2] < 3, f[i, 2], 0)), ", "))); }

Crossrefs

Cf. A046100, A013662, A360539.

Similar sequences: A382902, A382904, A382905, A382906.

Sequence in context: A367514 A270418 A056192 * A255693 A030107 A255593

Adjacent sequences: A382900 A382901 A382902 * A382904 A382905 A382906

Keyword

nonn,easy

Author

Amiram Eldar, Apr 08 2025

Status

approved