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A306797
Primitive abundant numbers (A071395) that are cubes.
3
6886512413632368153, 8815747507513708671, 334845050584968548307656, 1254177078562232856388071, 27869863573964698956703125
OFFSET
1,1
COMMENTS
The cube roots of the terms are 1902537, 2065791, 69440786, 107841591, 303187725, ...
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
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Mar 10 2019
STATUS
approved