A014840 Sum of all the digits of n in every base prime to n from 2 to n-1.

2, 2, 7, 2, 15, 10, 15, 8, 34, 12, 45, 22, 31, 32, 73, 28, 90, 40, 57, 50, 135, 46, 118, 74, 117, 70, 198, 58, 222, 120, 139, 122, 192, 92, 296, 152, 216, 136, 372, 112, 408, 202, 235, 208, 497, 176, 442, 224, 338, 260, 607, 202, 454, 276, 416, 330, 755, 194, 776

Offset: 3

Author

Olivier Gérard

Keywords

• nonn
• base
• look

Links

• Robert Israel, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A014836, A014837, A014838, A014839, A014841, A014842, A014843.

Programs

Maple

f:= proc(n) local b;
 add(convert(convert(n,base,b),`+`), b = select(t -> igcd(t,n)=1, [$2..n-1]))
end proc:
map(f, [$3..100]); # Robert Israel, Nov 08 2024

Mathematica

Table[Sum[If[CoprimeQ[i, n], Mod[Total[IntegerDigits[n, i]], n], 0], {i, 2, n-1}], {n, 3, 61}] (* Stefano Spezia, Sep 06 2022 *)

PARI

a(n) = {s = 0; for (i=2, n-1, if (gcd(i, n) == 1, d = digits(n, i); s += sum(j=1, #d, d[j]););); s;} \\ Michel Marcus, May 30 2014

Python

from math import gcd
from sympy.ntheory import digits
def a(n): return sum(sum(digits(n, b)[1:]) for b in range(2, n) if gcd(b, n) == 1)
print([a(n) for n in range(3, 62)]) # Michael S. Branicky, Sep 06 2022