A014838 Sum of all the digits of n in every prime base from 2 to n-1.

2, 3, 5, 6, 9, 11, 11, 10, 14, 16, 21, 21, 21, 23, 29, 32, 39, 42, 42, 39, 47, 52, 53, 49, 52, 53, 62, 66, 76, 83, 82, 76, 77, 82, 93, 87, 85, 90, 102, 107, 120, 123, 129, 120, 134, 144, 147, 153, 150, 151, 166, 176, 178, 185, 181, 168, 184, 194, 211, 199, 207

Offset: 3

Author

Olivier Gérard

Keywords

• nonn
• base

Crossrefs

Cf. A014836, A014837, A014839, A014840, A014841, A014842, A014843.

Programs

Mathematica

Table[Sum[If[PrimeQ[i], Mod[Total[IntegerDigits[n, i]], n], 0], {i, 2, n-1}],{n, 3, 63}] (* Stefano Spezia, Sep 06 2022 *)

PARI

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

Python

from sympy.ntheory import digits, isprime
def a(n): return sum(sum(digits(n, b)[1:]) for b in range(2, n) if isprime(b))
print([a(n) for n in range(3, 64)]) # Michael S. Branicky, Sep 06 2022