A222089 - OEIS

%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