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A080773
In binary representation: sum of number of 1's in prime factors of n (with repetition).
2
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
1,3
EXAMPLE
a(20) = a(2*2*5) = a('10' * '10' * '101') = 1+1+2 = 4.
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 *)
PROG
(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, hammingweight(f[k, 1])*f[k, 2]); \\ Michel Marcus, Aug 28 2019
CROSSREFS
Cf. A000120, A007088, A134599 (base 3).
Sequence in context: A202453 A259529 A196052 * A134598 A325120 A064515
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Mar 10 2003
STATUS
approved