A095413 - OEIS

%I #25 Apr 29 2022 20:48:49

%S 0,2,3,5,5,8,7,10,9,11,11,15,13,15,17,19,17,21,19,23,24,23,23,28,27,

%T 28,27,32,30,36,31,37,35,37,38,40,38,39,40,45,42,48,45,48,48,49,47,53,

%U 50,54,54,56,55,58,58,62,60,61,59,69,63,63,69,70,67,71,67

%N Total number of decimal digits of all distinct prime factors of the n-th repunit.

%H Max Alekseyev, <a href="/A095413/b095413.txt">Table of n, a(n) for n = 1..352</a> (first 322 terms from Giovanni Resta)

%F a(n) = A095407(A002275(n)).

%F a(n) < A095370(n) + n. - _Chai Wah Wu_, Nov 04 2019

%e n=10: 10th repunit = 1111111111 = 11*41*271*9091; distinct prime factors have a total of 11 decimal digits, so a(10)=11.

%e n=27: 27th repunit = 111111111111111111111111111 = 3^3*37*757*333667*440334654777631, with 28 prime factor digits, a(27)=28.

%t a[1] = 0; a[n_] := Total[IntegerLength /@ First /@ FactorInteger[(10^n - 1) /9]]; Array[a, 70] (* _Giovanni Resta_, Jul 09 2018 *)

%o (PARI) a(n) = vecsum(apply(x->#Str(x), factor((10^n-1)/9)[,1])); \\ _Michel Marcus_, Jul 09 2018

%Y Cf. A095414, A095415, A095416, A095417, A095418, A002275, A095407, A095370.

%K base,nonn

%O 1,2

%A _Labos Elemer_, Jun 22 2004