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

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, 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, 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

Offset: 1

Author

Antti Karttunen, Dec 30 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization

Crossrefs

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

Programs

Mathematica

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 *)

PARI

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)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A322867(n) = hammingweight(A122111(n));

Formula

a(n) = A000120(A122111(n)) = A000120(A322865(n)) = A001222(A322863(n)).