A366172 Strongly 2-near perfect numbers.

156, 352, 6832, 60976, 91648, 152812, 260865, 2834572, 3335968, 3532096, 4077388, 5044725, 5725504, 6112576, 8102656, 10557148, 19762876, 39411712, 50718016, 66965104, 111372508

Offset

1,1

Comments

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

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

Links

Table of n, a(n) for n=1..21.

Vedant Aryan, Dev Madhavani, Savan Parikh, Ingrid Slattery, and Joshua Zelinsky, On 2-Near Perfect Numbers, arXiv:2310.01305 [math.NT], 2023. See p. 13.

Example

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

Mathematica

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 *)

Prog

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

Crossrefs

Cf. A000203 (sigma).

Subsequence of A005835.

Intersection of A341475 and A334405.

Sequence in context: A065709 A037983 A298909 * A156849 A250382 A106056

Adjacent sequences: A366169 A366170 A366171 * A366173 A366174 A366175

Keyword

nonn,more

Author

Michel Marcus, Oct 03 2023

Extensions

a(21) from Ivan N. Ianakiev, Oct 04 2023

Status

approved