cp's OEIS Frontend

A318507 a(n) = A032742(n) XOR A001065(n)-A032742(n), where XOR is bitwise-or (A003987) and A001065 = sum of proper divisors and A032742 = the largest proper divisor of n.

%I A318507 #15 Sep 23 2018 21:30:15
%S A318507 1,1,1,3,1,0,1,7,2,6,1,12,1,4,1,15,1,5,1,6,3,8,1,20,4,14,13,0,1,20,1,
%T A318507 31,15,18,1,55,1,16,9,10,1,52,1,4,29,20,1,44,6,11,21,14,1,60,13,56,23,
%U A318507 30,1,80,1,28,1,63,11,12,1,58,19,4,1,115,1,38,1,60,3,20,1,106,22,42,1,72,23,40,25,28,1,78,5,48,27,44,21,92,1
%N A318507 a(n) = A032742(n) XOR A001065(n)-A032742(n), where XOR is bitwise-or (A003987) and A001065 = sum of proper divisors and A032742 = the largest proper divisor of n.
%C A318507 Note that here zeros occur only on even perfect numbers (even terms of A000396), in contrast to A318457, which would be zero also for any hypothetical odd perfect number. - _Antti Karttunen_, Aug 29 2018
%H A318507 Antti Karttunen, <a href="/A318507/b318507.txt">Table of n, a(n) for n = 1..65537</a>
%H A318507 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A318507 a(n) = A003987(A032742(n), A318505(n)).
%F A318507 For n > 1, a(n) = A001065(n) - 2*A318508(n).
%o A318507 (PARI)
%o A318507 A001065(n) = (sigma(n)-n);
%o A318507 A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
%o A318507 A318505(n) = if(1==n,0,A001065(n)-A032742(n));
%o A318507 A318507(n) = bitxor(A318505(n),A032742(n));
%Y A318507 Cf. A000396, A001065, A003987, A032742, A318505, A318506, A318508.
%Y A318507 Cf. also A106409, A318457, A318462, A318517.
%K A318507 nonn,base
%O A318507 1,4
%A A318507 _Antti Karttunen_, Aug 28 2018