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%I #18 Oct 11 2021 18:42:58
%S 0,1,1,2,1,2,1,3,2,2,2,3,2,2,2,4,2,3,2,3,2,3,2,4,2,3,3,3,2,3,2,5,3,3,
%T 2,4,2,3,3,4,2,3,2,4,3,3,2,5,2,3,3,4,2,4,3,4,3,3,2,4,2,3,3,6,3,4,2,4,
%U 3,3,2,5,2,3,3,4,3,4,2,5,4,3,2,4,3,3,3,5,2,4,3,4,3,3,3,6,2,3,4,4,3,4,3,5,3,3
%N Number of digits required to write the prime factors of n.
%H Charles R Greathouse IV, <a href="/A076649/b076649.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) is completely additive: a(m*n) = a(m)+a(n) for all integers m, n >= 1, with a(1)=0 and a(p^e) = e*floor(log_10(10*p)), p prime. - Diego Torres (torresvillarroel(AT)hotmail.com), Oct 26 2002
%F Totally additive with a(p) = A055642(p).
%e 12 = 2*2*3 so a(12)=3.
%t Join[{0},Table[Total[IntegerLength[#]&/@(Flatten[Table[#[[1]],#[[2]]]&/@ FactorInteger[n]])],{n,2,120}]] (* _Harvey P. Dale_, Mar 10 2018 *)
%o (PARI) a(n)=my(f=factor(n));sum(i=1,#f[,1],#Str(f[i,1])*f[i,2]) \\ _Charles R Greathouse IV_, Jul 24 2012
%Y Cf. A055642.
%K base,nonn
%O 1,4
%A _Jeff Burch_, Oct 24 2002
%E a(1) added, a(40) corrected by _Charles R Greathouse IV_, Jul 24 2012
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