A357699 Noncubefree numbers k such that A357698(k) > k.

24, 40, 72, 120, 168, 200, 264, 280, 312, 360, 392, 408, 440, 456, 504, 520, 540, 552, 600, 616, 680, 696, 728, 744, 760, 792, 840, 888, 920, 936, 952, 984, 1032, 1064, 1128, 1144, 1160, 1176, 1224, 1240, 1272, 1288, 1320, 1368, 1400, 1416, 1464, 1480, 1496, 1560

Offset

1,1

Comments

The cubefree numbers k such that A357698(k) > k are the cubefree abundant numbers (A357695).

The least odd term is (3/4) * prime(4)# * prime(11)# = 31588277195475.

The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 3, 32, 319, 3256, 32404, 323837, 3243328, 32425481, 324212022, ... . Apparently, the asymptotic density of this sequence exists and equals 0.0324... .

Links

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

Example

24 = 2^3 * 3 is a term since it is divisible by a cube and A357698(24) = 28 > 24.

Mathematica

f[p_, e_] := 1 + p + If[e == 1, 0, p^2]; q[n_] := AnyTrue[(fct = FactorInteger[n])[[;; , 2]], # > 2 &] && Times @@ f @@@ fct > n; Select[Range[2, 2000], q]

Prog

(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)) > n};

Crossrefs

Cf. A046099, A357695, A357698.

Sequence in context: A259217 A211567 A316271 * A328375 A141717 A185742

Adjacent sequences: A357696 A357697 A357698 * A357700 A357701 A357702

Keyword

nonn

Author

Amiram Eldar, Oct 10 2022

Status

approved