

A095414


Excess of total number of distinct prime factor digits of nth repunit over n, the number of digits of nth repunit itself.


6



1, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 3, 0, 1, 2, 3, 0, 3, 0, 3, 3, 1, 0, 4, 2, 2, 0, 4, 1, 6, 0, 5, 2, 3, 3, 4, 1, 1, 1, 5, 1, 6, 2, 4, 3, 3, 0, 5, 1, 4, 3, 4, 2, 4, 3, 6, 3, 3, 0, 9, 2, 1, 6, 6, 2, 5, 0, 6, 3, 5, 0, 6, 1, 3, 6, 3, 3, 5, 2, 7, 2, 3, 0, 10, 2, 4
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OFFSET

1,6


COMMENTS

a(n) <= A095370(n)  1 since the product of a k digit number and an m digit number has at least k+m1 digits.  Chai Wah Wu, Nov 03 2019


LINKS



FORMULA



EXAMPLE

n=9: r9 = 111111111 = 3*3*37*333667, with a total of 9 digits among the distinct prime factors; the excess is a(9) = 9  9 = 0;
n=30: r30 = 111....1111 = 3*7*11*13*31*37*41*211*241*271*2161*9091*2906161, with a total of 36 digits among the distinct prime factors, so the excess a(30) = 36  30 = 6.


MATHEMATICA

a[1] = 1; a[n_] := Total[IntegerLength /@ First /@ FactorInteger[(10^n  1)/9]]  n; Array[a, 60] (* Giovanni Resta, Jul 16 2018 *)


CROSSREFS



KEYWORD

sign,base


AUTHOR



EXTENSIONS



STATUS

approved



