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

1,4

Links

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

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).

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A055642.

Sequence in context: A344589 A153024 A066921 * A157235 A086289 A077807

Adjacent sequences: A076646 A076647 A076648 * A076650 A076651 A076652

Keyword

base,nonn

Author

Jeff Burch, Oct 24 2002

Extensions

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

Status

approved