A014837 Sum of all the digits of n in every base from 2 to n-1.

2, 3, 7, 9, 15, 16, 20, 24, 34, 33, 45, 51, 59, 57, 73, 72, 90, 91, 103, 113, 135, 127, 143, 155, 167, 170, 198, 192, 222, 220, 240, 256, 280, 260, 296, 314, 338, 332, 372, 366, 408, 415, 429, 451, 497, 471, 507, 514, 546, 555, 607, 597, 637, 633, 669, 697

Offset: 3

Author

Olivier Gérard

Keywords

• nonn
• base

Links

• Vincenzo Librandi, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A043306.

Programs

Mathematica

Table[Plus @@ Flatten[Table[IntegerDigits[n, b], {b, 2, n - 1}]], {n, 3, 36}] (* Alonso del Arte, Mar 28 2009 *)

Python

from sympy.ntheory.digits import digits
def a(n): return sum(sum(digits(n, b)[1:]) for b in range(2, n))
print([a(n) for n in range(3, 59)]) # Michael S. Branicky, Apr 04 2022

Formula

a(n) = A043306(n) - 1. - Amiram Eldar, Apr 16 2021