cp's OEIS Frontend

A323394 Carryless sum of divisors of n.

%I A323394 #16 Jan 18 2019 13:00:17
%S A323394 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,
%T A323394 20,36,20,52,32,43,48,44,38,51,38,40,46,70,42,76,44,74,58,62,48,84,47,
%U A323394 83,62,88,54,80,62,80,60,70,50,48,62,96,84,7,74,24,68,6
%N A323394 Carryless sum of divisors of n.
%C A323394 This sequence is a variant of A178910 for the base 10.
%H A323394 Rémy Sigrist, <a href="/A323394/b323394.txt">Table of n, a(n) for n = 1..19999</a>
%H A323394 Rémy Sigrist, <a href="/A323394/a323394.png">Scatterplot of the first 1000000 terms</a>
%H A323394 <a href="/index/Ca#CARRYLESS">Index entries for sequences related to carryless arithmetic</a>
%H A323394 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A323394 a(n) <= A000203(n).
%e A323394 For n = 42:
%e A323394 - the divisors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42,
%e A323394 - the sum of the units is: 1 + 2 + 3 + 6 + 7 + 4 + 1 + 2 = 26 == 6 (mod 10),
%e A323394 - the sum of the tens is: 1 + 2 + 4 = 7,
%e A323394 - hence a(42) = 76.
%e A323394 For n = 973:
%e A323394 - the divisors of 973 are: 1, 7, 139, 973,
%e A323394 - the sum of the units is: 1 + 7 + 9 + 3 = 20 == 0 (mod 10),
%e A323394 - the sum of the tens is: 3 + 7 = 10 == 0 (mod 10),
%e A323394 - the sum of the hundreds is: 1 + 9 = 10 == 0 (mod 10),
%e A323394 - hence a(973) = 0.
%p A323394 f:= proc(n) local t,d,dd,m,i;
%p A323394 t:= Vector(convert(n,base,10));
%p A323394 for d in numtheory:-divisors(n) minus {n} do
%p A323394   dd:= convert(d,base,10);
%p A323394   m:= nops(dd);
%p A323394   t[1..m]:= t[1..m] + Vector(dd) mod 10;
%p A323394 od:
%p A323394 add(t[i]*10^(i-1),i=1..ilog10(n)+1)
%p A323394 end proc:
%p A323394 map(f, [$1..100]); # _Robert Israel_, Jan 15 2019
%o A323394 (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)
%Y A323394 Cf. A000203, A169890, A178910, A323414 (positions of zeros), A323415 (fixed points).
%K A323394 nonn,base
%O A323394 1,2
%A A323394 _Rémy Sigrist_, Jan 13 2019