cp's OEIS Frontend

A239687 Numbers n such that if n = a U b (where U denotes concatenation) then abs(sigma*(a) - sigma*(b)) = abs(sigma*(n) - n), where sigma*(n) is the sum of the anti-divisors of n.

%I A239687 #10 Oct 14 2014 11:17:33
%S A239687 54,436,2014,2466,3365,4143,4965,7922,9332,15426,17554,24006,32874,
%T A239687 33574,39476,44296,49976,54118,83726,116174,137635,163964,164824,
%U A239687 177546,203514,220789,235434,379096,420716,476475,597741,600354,604986,680266,736306,748966
%N A239687 Numbers n such that if n = a U b (where U denotes concatenation) then abs(sigma*(a) - sigma*(b)) = abs(sigma*(n) - n), where sigma*(n) is the sum of the anti-divisors of n.
%C A239687 Neither a or b minor than 2 are considered because numbers 1 and 2 have no anti-divisors.
%C A239687 Similar to A239563 but using anti-divisors instead of divisors.
%e A239687 Anti-divisors of 4143 are 2, 5, 6, 1657, 2762 and their sum is 4432. Consider 4143 as 4 U 143. Anti-divisors of 4 is 3 and of 143 are 2, 3, 5, 7, 15, 19, 22, 26, 41, 57, 95 whose sum is 292. At the end we have that 4432 - 4143 = 289 = 292 - 3.
%p A239687 with(numtheory);
%p A239687 T:=proc(t) local w, x, y; x:=t; y:=0; while x>0 do x:=trunc(x/10); y:=y+1; od; end:
%p A239687 P:=proc(q) local a, b, c, d, f, g, i, j, k,n;
%p A239687 for n from 1 to q do b:=T(n); k:=0; j:=n; while j mod 2<>1 do k:=k+1; j:=j/2; od;
%p A239687 a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
%p A239687 for i from 1 to b-1 do c:=trunc(n/10^i); d:=n-c*10^i; if c>2 and d>2 then
%p A239687 k:=0; j:=c; while j mod 2<>1 do k:=k+1; j:=j/2; od;
%p A239687 f:=sigma(2*c+1)+sigma(2*c-1)+sigma(c/2^k)*2^(k+1)-6*c-2;
%p A239687 k:=0; j:=d; while j mod 2<>1 do k:=k+1; j:=j/2; od;
%p A239687 g:=sigma(2*d+1)+sigma(2*d-1)+sigma(d/2^k)*2^(k+1)-6*d-2;
%p A239687 if abs(f-g)=abs(a-n) then print(n); break; fi; fi; od; od; end: P(10^9);
%Y A239687 Cf. A066272, A066417, A239686.
%K A239687 nonn,base
%O A239687 1,1
%A A239687 _Paolo P. Lava_, Mar 24 2014