cp's OEIS Frontend

A095414 Excess of total number of distinct prime factor digits of n-th repunit over n, the number of digits of n-th repunit itself.

%I A095414 #23 Apr 29 2022 21:41:23
%S A095414 -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,
%T A095414 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,
%U A095414 3,5,0,6,1,3,6,3,3,5,2,7,2,3,0,10,2,4
%N A095414 Excess of total number of distinct prime factor digits of n-th repunit over n, the number of digits of n-th repunit itself.
%C A095414 a(n) <= A095370(n) - 1 since the product of a k digit number and an m digit number has at least k+m-1 digits. - _Chai Wah Wu_, Nov 03 2019
%H A095414 Max Alekseyev, <a href="/A095414/b095414.txt">Table of n, a(n) for n = 1..352</a> (first 322 terms from Giovanni Resta)
%F A095414 a(n) = A095407(A002275(n)) - n = A095413(n) - n.
%e A095414 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;
%e A095414 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.
%t A095414 a[1] = -1; a[n_] := Total[IntegerLength /@ First /@ FactorInteger[(10^n - 1)/9]] - n; Array[a, 60] (* _Giovanni Resta_, Jul 16 2018 *)
%Y A095414 Cf. A002275, A095370, A095407, A095413, A095415, A095416, A095417, A095418.
%K A095414 sign,base
%O A095414 1,6
%A A095414 _Labos Elemer_, Jun 22 2004
%E A095414 Data corrected by _Giovanni Resta_, Jul 16 2018