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%I #9 Mar 03 2016 04:49:34
%S 1,6,12,24,30,60,120,180,240,360,420,720,840,1260,1680,2520,4620,5040,
%T 7560,9240
%N Numbers n such that A114717(n) sets a new record.
%C This sequence gives yet another list of "increasingly compound" numbers.
%t b[s_] := b[s] = If[Length[s] < 2, 1, Sum[If[Length[Select[s, Mod[#, x] == 0 &]] == 1, b[Complement[s, {x}]], 0], {x, s}]]; a[n_] := a[n] = Module[{l, m}, l = Sort[FactorInteger[n], #1[[2]] > #2[[2]] &]; m = Product[Prime[i ]^l[[i]][[2]], {i, 1, Length[l]}]; b[Divisors[m] // Rest // Most]]; A119500 = Reap[For[record = 0; k = 1, k < 10^4, k++, ak = a[k]; If[ak > record, record = ak; Print[k, " ", ak]; Sow[k]]]][[2, 1]] (* _Jean-François Alcover_, Mar 03 2016, after _Alois P. Heinz_ *)
%Y Cf. A119499, A018894. Subset of A119840.
%K nonn
%O 1,2
%A _Antti Karttunen_, May 26 2006
%E a(11)-a(17) from _Alois P. Heinz_, Aug 06 2012
%E a(18)-a(20) from _Alois P. Heinz_, Feb 25 2016
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