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.

-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

Offset: 1

Author

Labos Elemer, Jun 22 2004

Keywords

• sign
• base

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A002275, A095370, A095407, A095413, A095415, A095416, A095417, A095418.

Programs

Mathematica

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

Formula

a(n) = A095407(A002275(n)) - n = A095413(n) - n.

Extensions

Data corrected by Giovanni Resta, Jul 16 2018