cp's OEIS Frontend

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).

%I A229883 #11 Feb 14 2021 18:35:20
%S A229883 1,2,5,8,11,30,34,172,311,498,562,602,630,1742,4608,4842,13664,16386,
%T A229883 24659,29150,56357,58185,86267,88114,242156,245325,839756,947942,
%U A229883 2524087,2963552,4218803,18281326,28292036,30023108,46376824,52058844,85990503,139548984
%N 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).
%C A229883 Tested up to k = 10^6.
%e A229883 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.
%p A229883 with(numtheory); P:=proc(q) local a,b,j,k,n; b:=0;
%p A229883 for n from 1 to q do a:=0;
%p A229883 for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then a:=a+k; fi; od;
%p A229883 b:=b+a; if b mod n=0 then print(n); fi; od; end: P(10^6);
%Y A229883 Cf. A056550, A066417.
%K A229883 nonn
%O A229883 1,2
%A A229883 _Paolo P. Lava_, Oct 02 2013
%E A229883 a(29)-a(38) from _Donovan Johnson_, Oct 12 2013