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A342924 Composite numbers k such that A003415(sigma(k)) = k + p*A003415(k), for some prime p, where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.

%I A342924 #19 Feb 25 2022 10:32:41
%S A342924 6,28,120,496,672,963,1036,5871,8128,10479,164284,264768,523776,
%T A342924 2308203,6511664,33550336,41240261,75384301,400902412,459818240,
%U A342924 581013140,1253768516,1476304896,2114464203,8589869056
%N A342924 Composite numbers k such that A003415(sigma(k)) = k + p*A003415(k), for some prime p, where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.
%C A342924 Composite numbers k for which A342926(k) = p*A003415(k), for some prime p.
%C A342924 Corresponding prime p for the first 25 terms is: 2, 2, 3, 2, 3, 3, 3, 11, 2, 11, 2, 3, 3, 5, 2, 2, 101, 397, 2, 3, 5, 7, 3, 5, 2. - _Antti Karttunen_, Feb 25 2022
%H A342924 <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>
%t A342924 Block[{f}, f[n_] := If[n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[n]]]; Select[Range[4, 10^6], And[CompositeQ[#], PrimeQ[(f[DivisorSigma[1, #]] - #)/f[#] ]] &]] (* _Michael De Vlieger_, Apr 08 2021 *)
%o A342924 (PARI)
%o A342924 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A342924 A342925(n) = A003415(sigma(n));
%o A342924 isA342924(n) = if((n<2)||isprime(n),0,my(q=(A342925(n)-n)/A003415(n)); ((1==denominator(q))&&isprime(q)));
%Y A342924 Odd terms in this sequence form a subsequence of A347884.
%Y A342924 Cf. A342925, A342926.
%Y A342924 Cf. A000396, A005820, A046060, A065997 (subsequences).
%Y A342924 Cf. also A342922, A342923, A007691.
%K A342924 nonn,more
%O A342924 1,1
%A A342924 _Antti Karttunen_, Apr 08 2021
%E A342924 Terms a(21) - a(25) from _Antti Karttunen_, Feb 25 2022