A095413 Total number of decimal digits of all distinct prime factors of the n-th repunit.

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, 28, 27, 32, 30, 36, 31, 37, 35, 37, 38, 40, 38, 39, 40, 45, 42, 48, 45, 48, 48, 49, 47, 53, 50, 54, 54, 56, 55, 58, 58, 62, 60, 61, 59, 69, 63, 63, 69, 70, 67, 71, 67

Offset: 1

Author

Labos Elemer, Jun 22 2004

Keywords

• base
• nonn

Examples

			n=10: 10th repunit = 1111111111 = 11*41*271*9091; distinct prime factors have a total of 11 decimal digits, so a(10)=11.
n=27: 27th repunit = 111111111111111111111111111 = 3^3*37*757*333667*440334654777631, with 28 prime factor digits, a(27)=28.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..352 (first 322 terms from Giovanni Resta)

Crossrefs

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

Programs

Mathematica

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

PARI

a(n) = vecsum(apply(x->#Str(x), factor((10^n-1)/9)[,1])); \\ Michel Marcus, Jul 09 2018

Formula

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

a(n) < A095370(n) + n. - Chai Wah Wu, Nov 04 2019