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Number of proper divisors of n is a square and sets a new record for such squares.
1

%I #12 May 09 2023 20:18:14

%S 1,2,16,48,6480,331776,26542080,207360000,174142586880,5476584960000,

%T 8352895346933760000,2556424320523960320000,190741334440500264960000,

%U 40745645800296001044480000,11921333402531266560000000000000000,58061203494913461453027322869401518080000

%N Number of proper divisors of n is a square and sets a new record for such squares.

%H Sean A. Irvine, <a href="/A063721/b063721.txt">Table of n, a(n) for n = 1..18</a>

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a063/A063721.java">Java program</a> (github)

%o (PARI) a=-1; for(n=1,10^7,x=numdiv(n)-1; if(issquare(x),b=x; if(b>a,a=b; print(n))))

%o (PARI) {a063721(m)=local(r,n,x); r=-1; for(n=1,m,x=numdiv(n)-1; if(issquare(x) && x>r,r=x; print1(n,","))) }

%Y Cf. A032741.

%K nonn

%O 1,2

%A _Jason Earls_, Aug 22 2001

%E More terms from _Don Reble_, May 12 2002

%E Missing a(12) inserted and a(16) from _Sean A. Irvine_, May 09 2023