A245649 - OEIS

%I #29 Mar 14 2018 03:48:21

%S 3,5,12,27,39,41,48,63,324,1275,1599,2259,2304,3124,3724,14295,19464,

%T 21659,40655,44659,262983,338064,485463,505407,686700,696795,898528,

%U 1595384,10377100,12332927,14452991,14883967,21024479,23068975,25527535,30971420,37471143

%N Numbers n such that the sum of the non-anti-divisors of n is a multiple of the sum of the anti-divisors of n.

%C Like A066860 but using anti-divisors.

%H Lars Blomberg, <a href="/A245649/b245649.txt">Table of n, a(n) for n = 1..70</a>

%e The anti-divisors of 14295 are 2, 6, 10, 11, 23, 30, 113, 253, 1243, 1906, 2599, 5718, 9530 which sum is 21444. The sum of the non-anti-divisors is 14295*14296 / 2 - 21444 = 102159216 and 102159216 / 21444 = 4764.

%p with(numtheory):P:=proc(q) local a,j,k,n;

%p for n from 3 to q do

%p k:=0; j:=n; while j mod 2 <> 1 do k:=k+1; j:=j/2; od;

%p a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;

%p if type(n*(n+1)/(2*a),integer) then print(n); fi;

%p od; end: P(10^10);

%Y Cf. A066272, A066860.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Aug 22 2014

%E a(28)-a(37) from _Lars Blomberg_, Oct 27 2014