A166722 -id:A166722 - cp's OEIS frontend

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

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

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)

			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

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

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

 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 *)

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

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

A354530 Numbers k such that k^2 is a minimal number; numbers k whose square is in A007416.

Original entry on oeis.org

1, 2, 4, 6, 8, 12, 24, 30, 32, 36, 60, 64, 72, 96, 120, 180, 192, 210, 216, 256, 288, 360, 420, 480, 512, 576, 768, 840, 864, 900, 960, 1080, 1260, 1440, 1536, 1680, 1728, 1800, 2048, 2304, 2520, 2880, 3360, 3840, 4320, 4608, 4620, 5400, 6144, 6300, 6720, 6912, 7200, 7560

Offset: 1

Jianing Song, Aug 16 2022

Numbers k such that there is no m < k^2 such that d(m) = d(k^2), d = A000005. Since only squares have an odd number of divisors, also numbers k such that there is no m < k such that d(m^2) = d(k^2).

			8 is a term since 8^2 = 64 has 7 divisors and no smaller number (smaller square) has that many divisors.

David A. Corneth, Table of n, a(n) for n = 1..14008 (first 310 terms from Jianing Song, terms <= 10^20).

Cf. A007416, A000005, A025487.
Square root of A166721. Also A016017 or A071571 sorted.
Cf. also A166722.

lista(nn) = {v = []; for (n=1, nn, d = numdiv(n^2); if (! vecsearch(v, d), print1(n, ", "); v = Set(concat(v, d))); ); } \\ from Michel Marcus's program for A166721

d(a(n)^2) = A166722(n).

cp's OEIS Frontend

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

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