A366172 - OEIS

%I #28 Sep 20 2024 02:17:55

%S 156,352,6832,60976,91648,152812,260865,2834572,3335968,3532096,

%T 4077388,5044725,5725504,6112576,8102656,10557148,19762876,39411712,

%U 50718016,66965104,111372508,232774912,483879808,2045453824,6849461025,7904670976,8521265152,11818720108,13112466688,13714642432

%N Strongly 2-near perfect numbers.

%C Integers k that have a divisor d such that sigma(k) - d - k/d = 2*k.

%C Note that this is not necessarily the same as just being the numbers that are strongly pseudoperfect and also 2-near perfect. This is because a number might be strongly pseudoperfect for one set of divisors which requires more than one redundant pair, while also being 2-near perfect due to removing a different pair. (This probably never actually happens.) - _Joshua Zelinsky_, Nov 09 2023

%H Vedant Aryan, Dev Madhavani, Savan Parikh, Ingrid Slattery, and Joshua Zelinsky, <a href="https://arxiv.org/abs/2310.01305">On 2-Near Perfect Numbers</a>, arXiv:2310.01305 [math.NT], 2023. See p. 13.

%e 156 is strongly 2-near perfect since sigma(156) = 392, 2*78 = 156, and 392-2-78 = 2*156.

%t fQ[n_]:=AnyTrue[Table[DivisorSigma[1,n]-Divisors[n][[i]]-n/Divisors[n][[i]],{i,DivisorSigma[0,n]}],#==2*n&]; Select[Range[61000],fQ[#]&] (* _Ivan N. Ianakiev_, Oct 04 2023 *)

%o (PARI) isok(k) = my(s=sigma(k)); fordiv(k, d, if (s-d-k/d == 2*k, return(1)));

%Y Cf. A000203 (sigma).

%Y Subsequence of A005835.

%Y Intersection of A341475 and A334405.

%K nonn

%O 1,1

%A _Michel Marcus_, Oct 03 2023

%E a(21) from _Ivan N. Ianakiev_, Oct 04 2023

%E a(22)-a(30) from _Amiram Eldar_, Sep 20 2024