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

1,1

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... .

Links

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

Example

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

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]

Prog

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

Crossrefs

Intersection of A004709 and A005231.

Intersection of A005408 and A357695.

A112643 is a subsequence.

Cf. A000203 (sigma), A333950.

Sequence in context: A045291 A125014 A333950 * A248694 A075460 A203087

Adjacent sequences: A357694 A357695 A357696 * A357698 A357699 A357700

Keyword

nonn

Author

Amiram Eldar, Oct 10 2022

Status

approved