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A334107 a(n) = A329697(A122111(n)).

%I A334107 #18 May 15 2020 02:04:53
%S A334107 0,0,0,1,0,1,0,1,2,1,0,1,0,1,2,2,0,2,0,1,2,1,0,2,3,1,2,1,0,2,0,2,2,1,
%T A334107 3,3,0,1,2,2,0,2,0,1,2,1,0,2,4,3,2,1,0,3,3,2,2,1,0,3,0,1,2,2,3,2,0,1,
%U A334107 2,3,0,3,0,1,3,1,4,2,0,2,4,1,0,3,3,1,2,2,0,3,4,1,2,1,3,2,0,4,2,4,0,2,0,2,3
%N A334107 a(n) = A329697(A122111(n)).
%H A334107 Antti Karttunen, <a href="/A334107/b334107.txt">Table of n, a(n) for n = 1..65537</a>
%F A334107 a(n) = A329697(A122111(n)) = A329697(A322865(n)).
%F A334107 a(n) = A329697(A105560(n)) + a(A064989(n)).
%F A334107 For n >= 1, a(A001248(n)) = n, and these seem to be also the first occurrences of each n.
%t A334107 Map[Length@ NestWhileList[# - #/FactorInteger[#][[-1, 1]] &, #, # != 2^IntegerExponent[#, 2] &] - 1 &, Array[Times @@ Table[Prime[LengthWhile[#1, # >= j &] /. 0 -> 1], {j, #2}] & @@ {#, Max[#]} &@ PrimePi@ Flatten[ConstantArray[#1, {#2}] & @@@ FactorInteger@ #] &, 105] ] (* _Michael De Vlieger_, May 14 2020, after _Robert G. Wilson v_ at A329697 *)
%o A334107 (PARI)
%o A334107 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A334107 A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
%o A334107 A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
%o A334107 A334107(n) = A329697(A122111(n));
%Y A334107 Cf. A001248, A008578 (positions of zeros), A064989, A105560, A122111, A322865, A329697, A334108, A334109, A334201.
%K A334107 nonn
%O A334107 1,9
%A A334107 _Antti Karttunen_, Apr 29 2020