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

Author

Rémy Sigrist, Jan 13 2019

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

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)

Crossrefs

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

Programs

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

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)

Formula

a(n) <= A000203(n).