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A322867 a(n) = A000120(A122111(n)). 6

%I #10 Dec 31 2018 13:23:09

%S 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 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 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 a(n) = A000120(A122111(n)).

%H Antti Karttunen, <a href="/A322867/b322867.txt">Table of n, a(n) for n = 1..20000</a>

%H Antti Karttunen, <a href="/A322867/a322867.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) = A000120(A122111(n)) = A000120(A322865(n)) = A001222(A322863(n)).

%t 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 (PARI)

%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 A322867(n) = hammingweight(A122111(n));

%Y Cf. A000120, A001222, A122111, A322863, A322865, A322866.

%K nonn

%O 1,4

%A _Antti Karttunen_, Dec 30 2018

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)