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%I #14 Jan 19 2019 12:46:16
%S 1,2,4,8,16,24,48,96,192,384,480,768,960,1920,3840,5760,7680,11520,
%T 19440,23040,26880,46080,53760,80640,107520,161280,215040,322560,
%U 612360,645120,967680,1224720,1290240,1935360,2580480,3870720,5160960,6451200,7096320
%N Where records occur in A222084.
%C Like A002182 but using tau#(n), as defined in A222084, instead of tau(n).
%e tau#(8)=4 and not until n=16 this value is overtaken: tau#(16)=5.
%p with(numtheory);
%p A222089:=proc(q)
%p local a,b,c,j,n,t;
%p t:=0;
%p for n from 1 to q do
%p a:=ifactors(n)[2]; b:=nops(a); c:=0;
%p for j from 1 to b do if a[j][1]^a[j][2]>c then c:=a[j][1]^a[j][2]; fi; od;
%p a:=op(sort([op(divisors(n))])); b:=nops(divisors(n));
%p for j from 1 to b do if a[j]=c then break; fi; od;
%p if j>t then t:=j; print(n); fi;
%p od; end:
%p A222089(10000000000);
%t f[n_]:= Module[{d = Divisors[n], k = 1}, While [LCM@@d[[1;;k]] != n, k++]; k]; fm=0; s={}; Do[f1=f[n]; If[f1>fm, fm=f1; AppendTo[s,n]], {n, 1, 10000}]; s (* _Amiram Eldar_, Jan 19 2019 *)
%o (PARI) f(n) = {my(d = divisors(n), k = 1); while (lcm(vector(k, j, d[j])) != n, k++); k; } \\ A222084
%o lista(nn) = {my(m=0, nm); for( n=1, nn, if ((nm=f(n)) > m, print1(n, ", "); m = nm););} \\ _Michel Marcus_, Jan 19 2019
%Y Cf. A000005, A000961, A001358, A003418, A005179, A024619, A034444, A077610, A222084, A222085.
%K nonn
%O 1,2
%A _Paolo P. Lava_, Feb 13 2013
%E a(2) inserted and a(32)-a(39) added by _Amiram Eldar_, Jan 19 2019
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