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A347874 Odd composites for which A342926(n) is even and A342926(2*n) is a multiple of 3.

%I A347874 #21 Aug 22 2025 10:55:22
%S A347874 45,153,261,325,369,405,441,477,801,909,925,1017,1233,1341,1377,1521,
%T A347874 1525,1557,1573,1773,1825,2097,2205,2313,2349,2401,2421,2425,2529,
%U A347874 2637,2725,2853,3177,3249,3321,3501,3609,3645,3757,3825,3925,4041,4149,4293,4477,4525,4581,4689,4825,5013,5121,5337,5445,5553,5725
%N A347874 Odd composites for which A342926(n) is even and A342926(2*n) is a multiple of 3.
%C A347874 Numbers k for which A347871(k) = 0 and A347883(2*k) = 0.
%C A347874 This is not a subsequence of A228058. The terms that do not occur there: 441, 1521, 2401, 3249, 8649, 16641, 28561, 35721, etc., seem all to be squares. Terms of A228058 missing from this sequence are: 117, 245, 333, 425, 549, 605, 637, 657, 725, etc. (See A351574.) Terms that are also in A228058 are given in A386429.
%H A347874 Antti Karttunen, <a href="/A347874/b347874.txt">Table of n, a(n) for n = 1..20000</a>
%H A347874 <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>
%t A347874 ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); f[n_] := ad[DivisorSigma[1, n]] - n; Select[Range[1, 5725, 2], CompositeQ[#] && EvenQ[f[#]] && Divisible[f[2*#], 3] &] (* _Amiram Eldar_, Sep 18 2021 *)
%o A347874 (PARI)
%o A347874 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A347874 A342926(n) = (A003415(sigma(n))-n);
%o A347874 isA347874(n) = ((n%2)&&!isprime(n)&&!(A342926(n)%2)&&!(A342926(2*n)%3));
%Y A347874 Cf. A000203, A003415, A228058, A342925, A342926, A347871, A347883, A351574, A386429 (subsequence).
%Y A347874 Intersection of A347872 and A351562.
%K A347874 nonn,changed
%O A347874 1,1
%A A347874 _Antti Karttunen_, Sep 18 2021