A080773 - OEIS

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

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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