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A036764 If n can be expressed as m/d(m) for some m, where d(m) is the number of divisors of m (A000005), then a(n) is the smallest such m, otherwise a(n) = 0.

%I A036764 #15 Oct 27 2023 22:00:43
%S A036764 1,8,9,36,40,72,56,80,108,180,88,240,104,252,360,128,136,0,152,480,
%T A036764 504,396,184,384,225,468,0,560,232,0,248,448,792,612,1260,864,296,684,
%U A036764 936,640,328,1680,344,880,0,828,376,1152,441,1800,1224,1040,424,972,1980
%N A036764 If n can be expressed as m/d(m) for some m, where d(m) is the number of divisors of m (A000005), then a(n) is the smallest such m, otherwise a(n) = 0.
%C A036764 If a(n) = q (say) is not zero, then x = q*d(x) has only a finite number of solutions. See A036763 for the numbers which cannot be expressible as m/d(m) for some m.
%C A036764 a(9p) = 0 for all primes p. - _Jianing Song_, Nov 25 2018
%H A036764 Nathaniel Johnston, <a href="/A036764/b036764.txt">Table of n, a(n) for n = 1..1250</a>
%e A036764 If q=25 then 25*9 = 225, 25*18 = 450 and 25*24 = 600 so that d(225), d(450), d(600) are 9, 18, 24, respectively. The smallest is 225. Thus a(25)=225.
%p A036764 with(numtheory): A036764 := proc(n) local k,p: for k from 1 to 4*n^2 do p:=n*k: if(p=n*tau(p))then return p: fi: od: return 0: end: seq(A036764(n),n=1..40); # _Nathaniel Johnston_, May 04 2011
%Y A036764 Cf. A000005, A033950, A036761-A036763, A051521.
%K A036764 nonn
%O A036764 1,2
%A A036764 _Labos Elemer_
%E A036764 Additional comments from _Asher Auel_, May 17 2001