A306796 Primitive abundant numbers (A071395) that are squares.

342225, 280495504, 1029447225, 1148667664, 1435045924, 1596961444, 1757705625, 2177622225, 14787776025, 18114198921, 32871503025, 45018230625, 150897287025, 245485566225, 272993710144, 296006724225, 705373218225, 1126920249225, 1329226832241, 1358425215225

Offset

1,1

Comments

The square roots of the terms are 585, 16748, 32085, 33892, 37882, 39962, 41925, 46665, 121605, 134589, ...

Links

Table of n, a(n) for n=1..20.

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=2; Do[If[papowerQ[m, e], AppendTo[s, m^e]], {m, 2, 50000}]; s

Crossrefs

Cf. A000290, A071395, A306797.

Sequence in context: A266171 A233604 A363175 * A365611 A029568 A235746

Adjacent sequences: A306793 A306794 A306795 * A306797 A306798 A306799

Keyword

nonn

Author

Amiram Eldar, Mar 10 2019

Status

approved