A369429 - OEIS

A369429

Square root of the largest square dividing the n-th powerful number.

1, 2, 2, 3, 4, 5, 3, 4, 6, 7, 8, 6, 9, 10, 6, 11, 5, 8, 12, 13, 14, 10, 6, 15, 9, 16, 12, 17, 18, 7, 19, 14, 20, 12, 21, 22, 10, 16, 23, 24, 25, 18, 15, 26, 27, 28, 20, 29, 12, 30, 31, 22, 18, 10, 32, 33, 15, 24, 34, 35, 36, 21, 11, 26, 37, 14, 38, 39, 28, 40

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OFFSET

1,2

LINKS

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

FORMULA

a(n) = A000188(A001694(n)).

a(n) > 1 for n >= 2.

Sum_{k=1..n} a(k) ~ c * n^2, where c = (15/(2*Pi^2))*(zeta(3)/zeta(3/2))^2 = 0.160894210785... .

MATHEMATICA

f[p_, e_] := p^Floor[e/2]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; s /@ Select[Range[2000], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]

(* or *)

f[p_, e_] := p^Floor[e/2]; f[p_, 1] := 0; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Array[s, 2000], # > 0 &]

PROG

(PARI) s(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] == 1, 0, f[i, 1]^(f[i, 2]\2))); }

lista(kmax) = {my(s1); for(k = 1, kmax, s1 = s(k); if(s1 > 0, print1(s1, ", "))); }

CROSSREFS

Cf. A000188, A001694, A087050, A369430.

Cf. A002117, A078434.

Sequence in context: A344568 A072813 A285106 * A120887 A155860 A318285

Adjacent sequences: A369426 A369427 A369428 * A369430 A369431 A369432

KEYWORD

nonn,easy

AUTHOR

Amiram Eldar, Jan 23 2024

STATUS

approved