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A080773 In binary representation: sum of number of 1's of 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..105.

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

Adjacent sequences:  A080770 A080771 A080772 * A080774 A080775 A080776

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Mar 10 2003

STATUS

approved

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Last modified June 5 23:10 EDT 2020. Contains 334858 sequences. (Running on oeis4.)