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A347884 Odd composites k for which A003415(sigma(k))-k is strictly positive and a multiple of A003415(k). Here A003415 is the arithmetic derivative.

%I A347884 #19 Sep 19 2021 22:02:12
%S A347884 963,969,5871,10479,2308203,41240261,52024391,69989429,75384301,
%T A347884 319255721,634457761,781718149,1184197307,1190942957,1195786661,
%U A347884 2114464203
%N A347884 Odd composites k for which A003415(sigma(k))-k is strictly positive and a multiple of A003415(k). Here A003415 is the arithmetic derivative.
%C A347884 Odd nonprimes k for which A343223(k) = A003415(k).
%C A347884 Any odd terms of A065997, including odd perfect numbers, odd triperfect numbers and odd 5-multiperfect numbers, should occur in this sequence, if such numbers exist at all.
%C A347884 The odd terms present in A342924 form a subsequence of this sequence.
%H A347884 <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>
%t A347884 ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); Select[Range[1, 2.5*10^6, 2], CompositeQ[#] && (d = ad[DivisorSigma[1, #]] - #) > 0 && Divisible[d, ad[#]] &] (* _Amiram Eldar_, Sep 19 2021 *)
%o A347884 (PARI)
%o A347884 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A347884 isA347884(n) = if(!(n%2)||isprime(n),0,my(u=(A003415(sigma(n))-(n))); ((u>0)&&!(u%A003415(n))));
%Y A347884 Cf. A000203, A003415, A007691, A065997, A342925, A342926, A343223.
%Y A347884 Subsequence of A343218.
%Y A347884 Cf. also A000396, A005820, A046060, A342922, A342923, A342924, A347872, A347880.
%K A347884 nonn,more
%O A347884 1,1
%A A347884 _Antti Karttunen_, Sep 19 2021