A306797 Primitive abundant numbers (A071395) that are cubes.

6886512413632368153, 8815747507513708671, 334845050584968548307656, 1254177078562232856388071, 27869863573964698956703125

Offset

1,1

Comments

The cube roots of the terms are 1902537, 2065791, 69440786, 107841591, 303187725, ...

Links

Table of n, a(n) for n=1..5.

Mathematica

abQ[f_] := Times@@((f[[;; , 1]]^(f[[;; , 2]]+1)-1)/(f[[;; , 1]]-1)) > 2*Times@@Power@@@f;
nondefQ[f_, g_] := Times@@((f^(g+1)-1)/(f-1)) >= 2*Times@@(f^g);
sub[f_, k_] := Module[{g=f[[;; , 2]]}, n=Length[g]; kk=k-1; Do[g[[i]] = Mod[kk, f[[i, 2]]+1]; kk=(kk-g[[i]])/(f[[i, 2]]+1), {i, 1, n}]; g];
paQ[f_] := abQ[f] && Module[{nd = Times@@(f[[;; , 2]]+1), ans=True}, Do[g=sub[f, k]; If[nondefQ[f[[;; , 1]], g], ans=False; Break[]], {k, 1, nd-1}]; ans];
papowerQ[n_, e_] := Module[{f=FactorInteger[n]}, f[[;; , 2]]*=e; paQ[f]];
s={}; e=3; Do[If[papowerQ[m, e], AppendTo[s, m^e]], {m, 2, 7*10^7}]; s

Crossrefs

Cf. A000578, A071395, A306796.

Sequence in context: A115530 A120317 A219283 * A213529 A187714 A222534

Adjacent sequences: A306794 A306795 A306796 * A306798 A306799 A306800

Keyword

nonn,more

Author

Amiram Eldar, Mar 10 2019

Status

approved