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%I #21 Feb 25 2022 11:38:06
%S 6,28,29,496,857,1721,8128,164284,6511664,33550336,400902412,
%T 8589869056
%N Numbers k such that A342925(k) = k + 2*A003415(k).
%C Question: Are all odd terms in A001359?
%C Certainly any prime p such that A003415(p+1) = p + 2 satisfies the equation. See comments in A007850.
%H <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>
%t Select[Range[2*10^5], #3 == #1 + 2 #2 & @@ Prepend[Map[If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &, {#, DivisorSigma[1, #]}], #] &] (* _Michael De Vlieger_, Feb 25 2022 *)
%o (PARI)
%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A342925(n) = A003415(sigma(n));
%o isA342922(n) = (A342925(n)==(n+(2*A003415(n))));
%Y Cf. A000396 (subsequence), A001359, A003415, A007850.
%Y Cf. A203617, A342923, A342924, A342925.
%K nonn,more
%O 1,1
%A _Antti Karttunen_, Apr 07 2021
%E Terms a(11) and a(12) from _Antti Karttunen_, Feb 25 2022
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