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A080773
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In binary representation: sum of number of 1's in prime factors of n (with repetition).
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2
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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
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OFFSET
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1,3
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LINKS
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EXAMPLE
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a(20) = a(2*2*5) = a('10' * '10' * '101') = 1+1+2 = 4.
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MATHEMATICA
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sn1[n_]:=Total[Flatten[IntegerDigits[#, 2]&/@Flatten[Table[#[[1]], {#[[2]]}] &/@ FactorInteger[n]]]]; Join[{0}, Rest[Array[sn1, 110]]] (* Harvey P. Dale, Nov 19 2013 *)
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PROG
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(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, hammingweight(f[k, 1])*f[k, 2]); \\ Michel Marcus, Aug 28 2019
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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