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 A306797 Primitive abundant numbers (A071395) that are cubes. 3
 6886512413632368153, 8815747507513708671, 334845050584968548307656, 1254177078562232856388071, 27869863573964698956703125 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 7 22:13 EDT 2024. Contains 375749 sequences. (Running on oeis4.)