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A324574 a(1) = 0; for n > 1, a(n) = A033879(A087207(n)).

%I A324574 #13 Mar 08 2019 20:15:12
%S A324574 0,1,1,1,1,2,1,1,1,4,1,2,1,5,0,1,1,2,1,4,2,16,1,2,1,18,1,5,1,6,1,1,-3,
%T A324574 46,-4,2,1,82,14,4,1,10,1,16,0,256,1,2,1,4,-12,18,1,2,-2,5,8,226,1,6,
%U A324574 1,748,2,1,-19,18,1,46,-12,12,1,2,1,1362,0,82,-12,22,1,4,1,3838,1,10,10,5458,254,16,1,6,-10,256,-348,12250
%N A324574 a(1) = 0; for n > 1, a(n) = A033879(A087207(n)).
%C A324574 As A087207 is a surjective function that toggles the parity, it follows that if it can be proved/disproved that a(n) = 0 for some/any even n, then it also proves/disproves the existence of odd perfect numbers.
%C A324574 The positions (n > 1) of zeros in squarefree n, 15, 385, ..., can be obtained as A019565(A000396(n)).
%H A324574 Antti Karttunen, <a href="/A324574/b324574.txt">Table of n, a(n) for n = 1..10000</a>
%H A324574 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324574 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A324574 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A324574 a(1) = 0; for n > 1, a(n) = A033879(A087207(n)).
%F A324574 a(n) = a(A007947(n)) = A324575(A007947(n)).
%o A324574 (PARI)
%o A324574 A033879(n) = (2*n-sigma(n));
%o A324574 A087207(n) = vecsum(apply(p->1<<primepi(p-1), factor(n)[, 1])); \\ From A087207
%o A324574 A324574(n) = if(1==n,0,A033879(A087207(n)));
%Y A324574 Cf. A000396, A007947, A033879, A019565, A087207, A324573, A324575.
%Y A324574 Cf. also A323244, A323174, A324546.
%K A324574 sign
%O A324574 1,6
%A A324574 _Antti Karttunen_, Mar 08 2019