A076649 Number of digits required to write the prime factors of n.

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, 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, 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

Offset: 1

Author

Jeff Burch, Oct 24 2002

Keywords

• base
• nonn

Examples

			12 = 2*2*3 so a(12)=3.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A055642.

Programs

Mathematica

Join[{0},Table[Total[IntegerLength[#]&/@(Flatten[Table[#[[1]],#[[2]]]&/@ FactorInteger[n]])],{n,2,120}]] (* Harvey P. Dale, Mar 10 2018 *)

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

Formula

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

Totally additive with a(p) = A055642(p).

Extensions

a(1) added, a(40) corrected by Charles R Greathouse IV, Jul 24 2012