A323394 Carryless sum of divisors of n.

1, 3, 4, 7, 6, 2, 8, 5, 3, 18, 12, 18, 14, 14, 14, 11, 18, 19, 10, 32, 22, 36, 24, 30, 21, 32, 20, 36, 20, 52, 32, 43, 48, 44, 38, 51, 38, 40, 46, 70, 42, 76, 44, 74, 58, 62, 48, 84, 47, 83, 62, 88, 54, 80, 62, 80, 60, 70, 50, 48, 62, 96, 84, 7, 74, 24, 68, 6

Offset

1,2

Comments

This sequence is a variant of A178910 for the base 10.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..19999

Rémy Sigrist, Scatterplot of the first 1000000 terms

Index entries for sequences related to carryless arithmetic

Index entries for sequences related to sigma(n)

Formula

a(n) <= A000203(n).

Example

For n = 42:
- the divisors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42,
- the sum of the units is: 1 + 2 + 3 + 6 + 7 + 4 + 1 + 2 = 26 == 6 (mod 10),
- the sum of the tens is: 1 + 2 + 4 = 7,
- hence a(42) = 76.
For n = 973:
- the divisors of 973 are: 1, 7, 139, 973,
- the sum of the units is: 1 + 7 + 9 + 3 = 20 == 0 (mod 10),
- the sum of the tens is: 3 + 7 = 10 == 0 (mod 10),
- the sum of the hundreds is: 1 + 9 = 10 == 0 (mod 10),
- hence a(973) = 0.

Maple

f:= proc(n) local t, d, dd, m, i;
t:= Vector(convert(n, base, 10));
for d in numtheory:-divisors(n) minus {n} do
  dd:= convert(d, base, 10);
  m:= nops(dd);
  t[1..m]:= t[1..m] + Vector(dd) mod 10;
od:
add(t[i]*10^(i-1), i=1..ilog10(n)+1)
end proc:
map(f, [$1..100]); # Robert Israel, Jan 15 2019

Prog

(PARI) a(n, base=10) = my (v=[]); fordiv (n, d, my (w=Vecrev(digits(d, base))); v=vector(max(#v, #w), k, (if (k>#v, w[k], k>#w, v[k], (v[k]+w[k])%base)))); fromdigits(Vecrev(v), base)

Crossrefs

Cf. A000203, A169890, A178910, A323414 (positions of zeros), A323415 (fixed points).

Sequence in context: A316570 A105853 A277216 * A348977 A017665 A248789

Adjacent sequences: A323391 A323392 A323393 * A323395 A323396 A323397

Keyword

nonn,base

Author

Rémy Sigrist, Jan 13 2019

Status

approved