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a(n) = A000265(A122111(n)).
9

%I #12 Dec 31 2018 13:22:54

%S 1,1,1,3,1,3,1,5,9,3,1,5,1,3,9,7,1,15,1,5,9,3,1,7,27,3,25,5,1,15,1,11,

%T 9,3,27,21,1,3,9,7,1,15,1,5,25,3,1,11,81,45,9,5,1,35,27,7,9,3,1,21,1,

%U 3,25,13,27,15,1,5,9,45,1,33,1,3,75,5,81,15,1,11,49,3,1,21,27,3,9,7,1,35,81,5,9,3,27,13,1,135,25,63,1,15,1,7,75

%N a(n) = A000265(A122111(n)).

%H Antti Karttunen, <a href="/A322865/b322865.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A322865/a322865.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = A000265(A122111(n)).

%F a(n) = A122111(A322820(n)).

%F A000005(a(n)) = A322813(n).

%F A000203(a(n)) = A322819(n).

%F A122111(a(n)) = A322820(n).

%F A000120(a(n)) = A322867(n).

%t Array[#/2^IntegerExponent[#, 2] &@ If[# < 3, 1, Block[{k = #, m = 0}, Times @@ Power @@@ Table[k -= m; k = DeleteCases[k, 0]; {Prime@ Length@ k, m = Min@ k}, Length@ Union@ k]] &@ Catenate[ConstantArray[PrimePi[#1], #2] & @@@ FactorInteger@ #]] &, 105] (* _Michael De Vlieger_, Dec 31 2018, after _JungHwan Min_ at A122111 *)

%o (PARI)

%o A000265(n) = (n>>valuation(n, 2));

%o 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 A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));

%o A322865(n) = A000265(A122111(n));

%Y Cf. A000265, A122111, A322813, A322819, A322820, A322826, A322865, A322867.

%K nonn

%O 1,4

%A _Antti Karttunen_, Dec 30 2018