A095418 Excess of sum of all decimal digits of distinct prime factors for n-th repunit over corresponding digit-sum for repunit itself (which is n).

-1, 0, 10, 0, 10, 20, 30, 17, 32, 26, 34, 35, 49, 53, 42, 51, 43, 74, 0, 56, 95, 77, 0, 81, 38, 94, 97, 106, 104, 80, 109, 123, 108, 96, 97, 132, 100, 65, 145, 136, 141, 184, 145, 173, 123, 99, 139, 172, 196, 120, 170, 176, 179, 213, 161, 169, 122, 201, 217, 184, 211, 216

Offset: 1

Author

Labos Elemer, Jun 22 2004

Keywords

• sign
• base

Examples

			n=60: concatenated distinct-prime factor-set for 60th-repunit is:
371113313741611012112412712161354190919901279612906161418890139526741,
its digit sum is 244, so a(60) = 244 - 60 = 184.
The value of this excess-sum is zero if n=2,4,19,23.
		

Links

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

Crossrefs

Cf. A095402, A002275, A095370, A095413, A095414, A095415, A095416, A095417.

Programs

Mathematica

a[1] = -1; a[n_] := Total@ Flatten[IntegerDigits /@ First /@ FactorInteger[(10^n - 1)/9]] - n; Array[a, 62] (* Giovanni Resta, Jul 19 2018 *)

Formula

a(n) = A095402(A002275(n)) - n = A095417(n) - n.

Extensions

Data corrected by Giovanni Resta, Jul 19 2018