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

3,1

Links

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

Formula

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

Maple

A014837 := proc(n)
    local a, b ;
    a := 0 ;
    for b from 2 to n-1 do
        a := a+ add(d, d=convert(n, base, b)) ;
    end do:
    a ;
end proc:
seq(A014837(n), n=3..20) ; # R. J. Mathar, May 22 2026

Mathematica

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

Prog

(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

Crossrefs

Cf. A043306.

Sequence in context: A392834 A096072 A305121 * A019312 A135369 A294283

Adjacent sequences: A014834 A014835 A014836 * A014838 A014839 A014840

Keyword

nonn,base

Author

Olivier Gérard

Status

approved