cp's OEIS Frontend

A322867 a(n) = A000120(A122111(n)).

%I A322867 #10 Dec 31 2018 13:23:09
%S A322867 1,1,1,2,1,2,1,2,2,2,1,2,1,2,2,3,1,4,1,2,2,2,1,3,4,2,3,2,1,4,1,3,2,2,
%T A322867 4,3,1,2,2,3,1,4,1,2,3,2,1,3,3,4,2,2,1,3,4,3,2,2,1,3,1,2,3,3,4,4,1,2,
%U A322867 2,4,1,2,1,2,4,2,3,4,1,3,3,2,1,3,4,2,2,3,1,3,3,2,2,2,4,3,1,4,3,6,1,4,1,3,4
%N A322867 a(n) = A000120(A122111(n)).
%H A322867 Antti Karttunen, <a href="/A322867/b322867.txt">Table of n, a(n) for n = 1..20000</a>
%H A322867 Antti Karttunen, <a href="/A322867/a322867.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A322867 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A322867 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A322867 a(n) = A000120(A122111(n)) = A000120(A322865(n)) = A001222(A322863(n)).
%t A322867 Array[DigitCount[#, 2, 1] &@ 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 A322867 (PARI)
%o A322867 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 A322867 A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
%o A322867 A322867(n) = hammingweight(A122111(n));
%Y A322867 Cf. A000120, A001222, A122111, A322863, A322865, A322866.
%K A322867 nonn
%O A322867 1,4
%A A322867 _Antti Karttunen_, Dec 30 2018