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.

8, 55, 26, 15, 43, 10, 89, 22, 20, 129, 118, 430, 43, 32, 39, 88, 174, 179, 35, 31, 45, 161, 53, 27, 228, 407, 122, 86, 90, 149, 87, 288, 46, 177, 283, 28, 117, 130, 222, 158, 200, 82, 68, 62, 383, 932, 32, 63, 120, 375, 1107, 67, 298, 110, 119, 352, 122, 277

Offset: 1

Author

Paolo P. Lava, Jan 24 2018

Keywords

• nonn
• easy

Examples

			a(1) = 8 because the sum of the anti-divisors of 8 is 8 and of 9 is 8 again;
a(2) = 55 because the sum of the anti-divisors of 55 is 74 and of 57 is 74 again.
		

Crossrefs

Cf. A007365, A066417.

Programs

Maple

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
k:=0; j:=n; while j mod 2 <> 1 do k:=k+1; j:=j/2; od;
a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
k:=0; j:=n+i; while j mod 2 <> 1 do k:=k+1; j:=j/2; od;
b:=sigma(2*(n+i)+1)+sigma(2*(n+i)-1)+sigma((n+i)/2^k)*2^(k+1)-6*(n+i)-2;
if a=b then print(n); break; fi; od; od; end: P(10^5);