A080773 In binary representation: sum of number of 1's in prime factors of n (with repetition).

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, 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, 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

Offset: 1

Author

Reinhard Zumkeller, Mar 10 2003

Keywords

• nonn
• base
• easy

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

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

PARI

a(n) = my(f=factor(n)); sum(k=1, #f~, hammingweight(f[k,1])*f[k,2]); \\ Michel Marcus, Aug 28 2019

Formula

Totally additive with a(p) = A000120(p). - Amiram Eldar, Jul 30 2025