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A175334 a(n) is the smallest positive divisor of Product_{k=1..n} d(k) that does not yet occur in the sequence, where d(k) is the number of positive divisors of k.

%I A175334 #12 Mar 25 2019 02:31:55
%S A175334 1,2,4,3,6,8,12,16,9,18,24,27,32,36,48,5,10,15,20,30,40,45,54,60,64,
%T A175334 72,80,81,90,96,108,120,128,135,144,160,162,180,192,216,240,243,256,
%U A175334 270,288,320,324,25,50,75,100,150,200,225,300,360,384,400,405,432,450,480
%N A175334 a(n) is the smallest positive divisor of Product_{k=1..n} d(k) that does not yet occur in the sequence, where d(k) is the number of positive divisors of k.
%C A175334 This sequence is a permutation of the positive integers.
%p A175334 From _R. J. Mathar_, Aug 31 2010: (Start)
%p A175334 A066843 := proc(n) option remember; if n <= 2 then n; else procname(n-1) * numtheory[tau](n) ; end if; end proc:
%p A175334 A175334 := proc(n) option remember ; dvs := sort(convert(numtheory[divisors](A066843(n)),list)) ; for d in dvs do wrks := true; for i from 1 to n-1 do if procname(i) = d then wrks := false; break; end if; end do: if wrks then return d; end if; end do: end proc:
%p A175334 seq(A175334(n),n=1..90) ; (End)
%Y A175334 Cf. A066843.
%K A175334 nonn
%O A175334 1,2
%A A175334 _Leroy Quet_, Apr 14 2010
%E A175334 More terms from _R. J. Mathar_, Aug 31 2010