A229883 Numbers k such that Sum_{j=1..k} sigma_*(j) == 0 (mod k), where sigma_*(j) is the sum of the anti-divisors of j (A066417).

1, 2, 5, 8, 11, 30, 34, 172, 311, 498, 562, 602, 630, 1742, 4608, 4842, 13664, 16386, 24659, 29150, 56357, 58185, 86267, 88114, 242156, 245325, 839756, 947942, 2524087, 2963552, 4218803, 18281326, 28292036, 30023108, 46376824, 52058844, 85990503, 139548984

Offset: 1

Author

Paolo P. Lava, Oct 02 2013

Keywords

• nonn

Comments

Tested up to k = 10^6.

Examples

			The sum of the anti-divisors of the numbers from 1 to 8 is 0 + 0 + 2 + 3 + 5 + 4 + 10 + 8 = 32 and 32/8 = 4.
		

Crossrefs

Cf. A056550, A066417.

Programs

Maple

with(numtheory); P:=proc(q) local a,b,j,k,n; b:=0;
for n from 1 to q do a:=0;
for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then a:=a+k; fi; od;
b:=b+a; if b mod n=0 then print(n); fi; od; end: P(10^6);

Extensions

a(29)-a(38) from Donovan Johnson, Oct 12 2013