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A166721 Squares for which no smaller square has the same number of divisors.

%I A166721 #30 Nov 28 2023 08:38:50
%S A166721 1,4,16,36,64,144,576,900,1024,1296,3600,4096,5184,9216,14400,32400,
%T A166721 36864,44100,46656,65536,82944,129600,176400,230400,262144,331776,
%U A166721 589824,705600,746496,810000,921600,1166400,1587600,2073600,2359296,2822400,2985984,3240000
%N A166721 Squares for which no smaller square has the same number of divisors.
%C A166721 From _Jon E. Schoenfield_, Mar 03 2018: (Start)
%C A166721 Numbers k^2 such there is no positive m < k such that A000005(m^2) = A000005(k^2).
%C A166721 Square terms in A007416. (End)
%H A166721 Amiram Eldar, <a href="/A166721/b166721.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..300 from Alois P. Heinz)
%e A166721 The positive squares begin 1, 4, 9, 16, 25, 36, 49, 64, ..., and their corresponding numbers of divisors are 1, 3, 3, 5, 3, 9, 3, 7, ...; thus, a(1)=1, a(2)=4, 9 is not a term (it has the same number of divisors as does 4; the same is true of 25, 49, etc.), a(3)=16, a(4)=36, a(5)=64, ... - _Jon E. Schoenfield_, Mar 03 2018
%t A166721  Sort[Module[{nn=2000,tbl},tbl=Table[{n^2,DivisorSigma[0,n^2]},{n,nn}];Table[ SelectFirst[ tbl,#[[2]]==k&],{k,nn}]][[All,1]]/."NotFound"->Nothing] (* _Harvey P. Dale_, Jun 06 2022 *)
%o A166721 (PARI) lista(nn) = {v = []; for (n=1, nn, d = numdiv(n^2); if (! vecsearch(v, d), print1(n^2, ", "); v = Set(concat(v, d))););} \\ _Michel Marcus_, Mar 04 2018
%Y A166721 Cf. A000005, A005179, A007416, A025487, A048691, A136404, A166722.
%K A166721 easy,nonn
%O A166721 1,2
%A A166721 Alexander Isaev (i2357(AT)mail.ru), Oct 20 2009
%E A166721 Proper definition and substantial editing by _Jon E. Schoenfield_, Mar 03 2018