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A347872 Numbers k such that k and A003415(sigma(k)) have the same parity.

%I A347872 #15 Sep 11 2024 16:17:40
%S A347872 5,6,8,9,12,13,14,17,18,22,24,25,28,29,30,36,37,38,41,42,44,45,46,48,
%T A347872 50,53,54,56,60,61,62,66,70,73,76,78,84,86,88,89,92,94,96,97,100,101,
%U A347872 102,108,109,110,112,113,114,117,118,120,124,126,130,132,134,137,138,140,142,144,149,150,152,153,154,156,157
%N A347872 Numbers k such that k and A003415(sigma(k)) have the same parity.
%C A347872 Numbers k for which A347870(k) is equal to A000035(k).
%H A347872 Robert Israel, <a href="/A347872/b347872.txt">Table of n, a(n) for n = 1..10000</a>
%H A347872 <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>
%p A347872 ader:= proc(n) local F,t;
%p A347872   F:= ifactors(n)[2];
%p A347872   add(t[2]*n/t[1], t= F)
%p A347872 end proc:
%p A347872 filter:= n -> n - ader(numtheory:-sigma(n)) mod 2 = 0:
%p A347872 select(filter, [$1..1000]); # _Robert Israel_, Sep 11 2024
%t A347872 ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); Select[Range[157], Mod[ad[DivisorSigma[1, #]], 2] == Mod[#, 2] &] (* _Amiram Eldar_, Sep 18 2021 *)
%Y A347872 Cf. A000035, A000203, A003415, A342925, A347870.
%Y A347872 Positions of zeros in A347871. Cf. A347873 for complement.
%Y A347872 Cf. A000396, A342922, A347874 (subsequences).
%Y A347872 Cf. also A347883.
%K A347872 nonn
%O A347872 1,1
%A A347872 _Antti Karttunen_, Sep 17 2021