A014838 -id:A014838 - cp's OEIS frontend

A014841 Sum modulo the base of all the digits of n in every base from 2 to n-1.

0, 3, 2, 7, 6, 13, 13, 18, 19, 31, 24, 37, 40, 48, 48, 65, 59, 79, 76, 85, 93, 117, 105, 121, 132, 148, 143, 176, 163, 193, 191, 208, 226, 250, 225, 262, 277, 302, 290, 332, 320, 359, 363, 376, 394, 444, 419, 455, 462, 491, 495, 551, 540, 577, 564, 601, 625

Offset: 3

Olivier Gérard

Stefano Spezia, Table of n, a(n) for n = 3..10000

Cf. A014836, A014837, A014838, A014839, A014840, A014842, A014843.

Table[Sum[Mod[Total[IntegerDigits[n,i]], i], {i,2,n-1}], {n,3,59}] (* Stefano Spezia, Sep 06 2022 *)

a(n) = sum(b=2, n-1, sumdigits(n, b) % b); \\ Michel Marcus, Sep 06 2022

from sympy.ntheory import digits
def a(n): return sum(sum(digits(n, b)[1:])%b for b in range(2, n))
print([a(n) for n in range(3, 60)]) # Michael S. Branicky, Sep 06 2022

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

Original entry on oeis.org

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

Olivier Gérard

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

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

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

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 *)

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

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

A014839 Sum of all the digits of n in every prime-power base from 2 to n-1.

Original entry on oeis.org

2, 3, 7, 9, 13, 13, 16, 19, 26, 28, 36, 39, 42, 34, 45, 44, 55, 59, 63, 64, 76, 75, 80, 82, 82, 87, 102, 112, 128, 113, 120, 121, 129, 130, 148, 149, 154, 156, 175, 187, 207, 214, 219, 217, 238, 227, 237, 228, 233, 239, 262, 246, 256, 261, 265, 260, 284, 299

Offset: 3

Olivier Gérard

Cf. A014836, A014837, A014838, A014840, A014841, A014842, A014843.

Table[Sum[If[PrimePowerQ[i], Mod[Total[IntegerDigits[n, i]], n], 0], {i, 2, n-1}], {n, 3, 60}] (* Stefano Spezia, Sep 06 2022 *)

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A014841 Sum modulo the base of all the digits of n in every base from 2 to n-1.

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

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Python

A014839 Sum of all the digits of n in every prime-power base from 2 to n-1.

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Mathematica