A357697 Odd cubefree abundant numbers.

1575, 2205, 3465, 4095, 5355, 5775, 5985, 6435, 6825, 7245, 8085, 8415, 8925, 9135, 9555, 9765, 11025, 11655, 12705, 12915, 13545, 14805, 15015, 16695, 17325, 18585, 19215, 19635, 20475, 21105, 21945, 22365, 22995, 23205, 24255, 24885, 25935, 26145, 26565, 26775

Offset: 1

Author

Amiram Eldar, Oct 10 2022

Keywords

• nonn

Comments

First differs from A333950 at n = 1258. Terms that are not in A333950 include 8564325, 8565795, 8567325, ... and terms of A333950 that are not here include 1126125, 2096325, 2207205, ... .

The numbers of terms not exceeding 10^k, for k = 4, 5, ..., are 16, 125, 1127, 11734, 116911, 1162781, 11638566, 116342286, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00116... .

Examples

			1575 = 3^2 * 5^2 * 7 is a term since it is odd and cubefree and sigma(1575) = 3224 > 2*1575.
		

Links

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

Crossrefs

Intersection of A004709 and A005231.

Intersection of A005408 and A357695.

A112643 is a subsequence.

Cf. A000203 (sigma), A333950.

Programs

Mathematica

f[p_, e_] := (p^(e+1)-1)/(p-1); q[1] = 0; q[n_] := AllTrue[(fct = FactorInteger[n])[[;;, 2]], # < 3 &] && Times @@ f @@@ fct > 2*n; Select[Range[1, 30000, 2], q]

PARI

is(n) = {my(f); if(n%2 == 0, return(0)); f = factor(n); (n==1 || vecmax(f[,2]) < 3) && sigma(f, -1) > 2};