A080773 - OEIS

%I #16 Jan 22 2022 18:21:42

%S 0,1,2,2,2,3,3,3,4,3,3,4,3,4,4,4,2,5,3,4,5,4,4,5,4,4,6,5,4,5,5,5,5,3,

%T 5,6,3,4,5,5,3,6,4,5,6,5,5,6,6,5,4,5,4,7,5,6,5,5,5,6,5,6,7,6,5,6,3,4,

%U 6,6,4,7,3,4,6,5,6,6,5,6,8,4,4,7,4,5,6,6,4,7,6,6,7,6,5,7,3,7,7,6,4,5,5,6,7

%N In binary representation: sum of number of 1's in prime factors of n (with repetition).

%e a(20) = a(2*2*5) = a('10' * '10' * '101') = 1+1+2 = 4.

%t sn1[n_]:=Total[Flatten[IntegerDigits[#,2]&/@Flatten[Table[#[[1]],{#[[2]]}] &/@ FactorInteger[n]]]]; Join[{0},Rest[Array[sn1,110]]] (* _Harvey P. Dale_, Nov 19 2013 *)

%o (PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, hammingweight(f[k,1])*f[k,2]); \\ _Michel Marcus_, Aug 28 2019

%Y Cf. A000120, A007088, A134599 (base 3).

%K nonn,base

%O 1,3

%A _Reinhard Zumkeller_, Mar 10 2003