A357700 Noncubefree numbers k such that A073185(k) > 2*k.

360360, 471240, 1801800, 2356200, 2522520, 2633400, 2784600, 3112200, 3187800, 3298680, 3686760, 3767400, 3898440, 3963960, 4019400, 4296600, 4462920, 4684680, 5128200, 5183640, 5682600, 5793480, 6126120, 6846840, 8011080, 8288280, 8953560, 10210200, 10450440

Offset: 1

Author

Amiram Eldar, Oct 10 2022

Keywords

• nonn

Comments

The cubefree numbers k such that A073185(k) > 2*k are the cubefree abundant numbers (A357695).

The least odd term is (3/4) * prime(13)# * prime(197)# = 6.252...*10^517.

Examples

			360360 = 2^3 * 45045 is a term since it is divisible by a cube and A073185(360360) = 733824 > 2*360360.
		

Links

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

Crossrefs

Cf. A073185, A357695.

Programs

Mathematica

f[p_, e_] := 1 + p + If[e == 1, 0, p^2]; q[n_] := AnyTrue[(fct = FactorInteger[n])[[;;, 2]], # > 2 &] && Times @@ f @@@ fct > 2*n; Select[Range[2, 5*10^6], q]

PARI

is(n) = {my(f = factor(n)); if(n == 1 || vecmax(f[,2]) < 3, return(0)); prod(i=1, #f~, 1 + f[i,1] + if(f[i,2]==1, 0, f[i,1]^2)) > 2*n};