cp's OEIS Frontend

A378988 a(n) = 2*n XOR 1+sigma(n), where XOR is bitwise-xor, A003987.

%I A378988 #36 Dec 16 2024 19:15:05
%S A378988 0,0,3,0,13,1,7,0,28,7,27,5,21,5,7,0,49,12,51,3,11,9,55,13,18,31,31,1,
%T A378988 37,117,31,0,115,115,119,20,109,113,119,11,121,53,123,13,21,21,111,29,
%U A378988 88,58,47,11,93,21,39,9,35,47,75,209,69,29,23,0,215,21,195,247,235,29,199,84,217,231,235,21,251,53,207
%N A378988 a(n) = 2*n XOR 1+sigma(n), where XOR is bitwise-xor, A003987.
%C A378988 For any hypothetical quasiperfect number q (for which sigma(q) = 2*q+1, see A336701), a(q) would be equal to 2*q XOR 2*q+2 = 2*(q XOR q+1) = 2*A038712(1+q) = A100892(1+q).
%C A378988 See also A000079 and A235796 concerning the "almost perfect" or "least deficient" numbers that give positions of 0's here.
%H A378988 Antti Karttunen, <a href="/A378988/b378988.txt">Table of n, a(n) for n = 1..32768</a>
%H A378988 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A378988 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A378988 For all n in A028983, a(n) = 2n+1 XOR sigma(n) = 1+A318467(n).
%t A378988 Array[BitXor[2*#, DivisorSigma[1, #] + 1] &, 100] (* _Paolo Xausa_, Dec 16 2024 *)
%o A378988 (PARI) A378988(n) = bitxor(n+n,1+sigma(n));
%Y A378988 Cf. A000079 (conjectured to give positions of all 0's), A000396 (positions of 1's), A000203, A003987, A028982 (positions of even terms), A028983 (of odd terms), A038712, A100892, A318467, A336701, A378998, A379009 [= a(n^2)].
%Y A378988 Cf. also A235796, A294898, A294899, A318457.
%K A378988 nonn,look
%O A378988 1,3
%A A378988 _Antti Karttunen_, Dec 16 2024