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

1, 4, 16, 36, 64, 144, 576, 900, 1024, 1296, 3600, 4096, 5184, 9216, 14400, 32400, 36864, 44100, 46656, 65536, 82944, 129600, 176400, 230400, 262144, 331776, 589824, 705600, 746496, 810000, 921600, 1166400, 1587600, 2073600, 2359296, 2822400, 2985984, 3240000

Offset

1,2

Comments

From Jon E. Schoenfield, Mar 03 2018: (Start)

Numbers k^2 such there is no positive m < k such that A000005(m^2) = A000005(k^2).

Square terms in A007416. (End)

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..300 from Alois P. Heinz)

Example

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

Mathematica

 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 *)

Prog

(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

Crossrefs

Cf. A000005, A005179, A007416, A025487, A048691, A136404, A166722.

Sequence in context: A238259 A373559 A063755 * A085040 A030179 A207025

Adjacent sequences: A166718 A166719 A166720 * A166722 A166723 A166724

Keyword

easy,nonn

Author

Alexander Isaev (i2357(AT)mail.ru), Oct 20 2009

Extensions

Proper definition and substantial editing by Jon E. Schoenfield, Mar 03 2018

Status

approved