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A277802 The least k > 0 such that k*A004709(n) is a cube. 2
1, 4, 9, 2, 25, 36, 49, 3, 100, 121, 18, 169, 196, 225, 289, 12, 361, 50, 441, 484, 529, 5, 676, 98, 841, 900, 961, 1089, 1156, 1225, 6, 1369, 1444, 1521, 1681, 1764, 1849, 242, 75, 2116, 2209, 7, 20, 2601, 338, 2809, 3025, 3249, 3364, 3481, 450, 3721, 3844 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is a permutation of the cubefree numbers (A004709).

a(n) <= A004709(n)^2, with equality iff A004709(n) is squarefree. - Robert Israel, Nov 09 2016

LINKS

Peter Kagey, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A048798(A004709(n)).

EXAMPLE

a(8) = 3 because 3 * A004709(8) = 3 * 9 = 3^3.

a(16) = 12 because A004709(16) = 18 = 2^1 * 3^2. The least k such that k * 2^1 * 3^2 is a cube is 2^(3 - (1 mod 3)) * 3^(3 - (2 mod 3)) = 12. - David A. Corneth, Nov 01 2016

MAPLE

f:= proc(n) local F, E;

   F:= ifactors(n)[2];

   E:= F[.., 2];

   if max(E) >= 3 then return NULL fi;

   mul(F[i, 1]^(3-E[i]), i=1..nops(F));

end proc:

map(f, [$1..1000]); # Robert Israel, Nov 09 2016

MATHEMATICA

Table[k = 1; While[! IntegerQ[(k #)^(1/3)], k++] &@ #[[n]]; k, {n, 53}] &@ Select[Range[10^4], FreeQ[FactorInteger@ #, {_, k_ /; k > 2}] &] (* Michael De Vlieger, Nov 01 2016, after Jan Mangaldan at A004709 *)

PROG

(PARI) \\ A list of about n terms (a little more probably).

lista(n) = {n = ceil(1.21*n); my(l=List([1]), f); forprime(p=2, n, for(i=1, #l, if(l[i] * p<=n, listput(l, l[i]*p); if(l[i]*p^2<=n, listput(l, l[i]*p^2))))); listsort(l); for(i=2, #l, f=factor(l[i]); f[, 2] = vector(#f[, 2], i, 3-(f[i, 2] % 3))~; l[i] = factorback(f)); l} \\ David A. Corneth, Nov 01 2016

CROSSREFS

Cf. A048798, A004709.

Sequence in context: A048798 A007914 A048758 * A159253 A011262 A073843

Adjacent sequences:  A277799 A277800 A277801 * A277803 A277804 A277805

KEYWORD

nonn,look

AUTHOR

Peter Kagey, Oct 31 2016

STATUS

approved

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Last modified April 20 06:57 EDT 2021. Contains 343121 sequences. (Running on oeis4.)