cp's OEIS Frontend

A298654 Least number k such that the sum of the anti-divisors of k is equal to the sum of the anti-divisors of k+n.

%I A298654 #7 Jan 28 2018 13:27:36
%S A298654 8,55,26,15,43,10,89,22,20,129,118,430,43,32,39,88,174,179,35,31,45,
%T A298654 161,53,27,228,407,122,86,90,149,87,288,46,177,283,28,117,130,222,158,
%U A298654 200,82,68,62,383,932,32,63,120,375,1107,67,298,110,119,352,122,277
%N A298654 Least number k such that the sum of the anti-divisors of k is equal to the sum of the anti-divisors of k+n.
%e A298654 a(1) = 8 because the sum of the anti-divisors of 8 is 8 and of 9 is 8 again;
%e A298654 a(2) = 55 because the sum of the anti-divisors of 55 is 74 and of 57 is 74 again.
%p A298654 with(numtheory): P:=proc(q) local a,b,i,j,k,n; for i from 0 to q do for n from 1 to q do
%p A298654 k:=0; j:=n; while j mod 2 <> 1 do k:=k+1; j:=j/2; od;
%p A298654 a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
%p A298654 k:=0; j:=n+i; while j mod 2 <> 1 do k:=k+1; j:=j/2; od;
%p A298654 b:=sigma(2*(n+i)+1)+sigma(2*(n+i)-1)+sigma((n+i)/2^k)*2^(k+1)-6*(n+i)-2;
%p A298654 if a=b then print(n); break; fi; od; od; end: P(10^5);
%Y A298654 Cf. A007365, A066417.
%K A298654 nonn,easy
%O A298654 1,1
%A A298654 _Paolo P. Lava_, Jan 24 2018