cp's OEIS Frontend

A192284 Numbers n such that the average of the anti-divisors of n is an integer.

%I A192284 #9 Jan 13 2025 04:10:49
%S A192284 3,4,6,8,9,11,15,16,18,19,20,26,29,30,34,36,37,38,47,49,51,63,64,68,
%T A192284 69,82,93,94,95,96,106,117,120,121,131,134,135,141,155,169,174,186,
%U A192284 187,190,191,197,200,203,206,224,226,244,252,257,271,272,274,276,289
%N A192284 Numbers n such that the average of the anti-divisors of n is an integer.
%C A192284 Like A003601 but using anti-divisors.
%H A192284 Paolo P. Lava, <a href="/A192284/b192284.txt">Table of n, a(n) for n = 1..1000</a>
%e A192284 Anti-divisors of 38 are 7: 3, 4, 5, 7, 11, 15, 25. Their sum is 70 and 70/7=10 that is an integer.
%p A192284 with(numtheory);
%p A192284 P:=proc(n)
%p A192284 local a,b,i,k;
%p A192284 for i from 3 to n do
%p A192284   a:=0; b:=0;
%p A192284   for k from 2 to i-1 do
%p A192284     if abs((i mod k)- k/2) < 1 then a:=a+k; b:=b+1; fi;
%p A192284   od;
%p A192284   if trunc(a/b)=a/b then print(i); fi;
%p A192284 od;
%p A192284 end:
%p A192284 P(1000);
%Y A192284 Cf. A003601, A066272.
%K A192284 nonn
%O A192284 1,1
%A A192284 _Paolo P. Lava_, Jul 20 2011