This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A305617 #16 Dec 23 2024 09:54:02
%S A305617 3,9,27,35,39,55,81,243,279,387,715,729,1443,2187,2619,3655,5635,6561,
%T A305617 10855,12635,19683,59049,77283,177147,178119,294759,443135,531441,
%U A305617 817167,1170723,1594323,1605987,1632231,1710963,1947159,2410239,2624375,2655747,3944255
%N A305617 Deficient 2-hyperperfect numbers: numbers k such that 3*k/2 + 1/2 - sigma(k) is a proper divisor of k.
%C A305617 Includes all the powers of 3 (A000244).
%C A305617 A combination of the notions 2-hyperperfect numbers (A007593) and deficient-perfect numbers (A271816).
%H A305617 Amiram Eldar, <a href="/A305617/b305617.txt">Table of n, a(n) for n = 1..74</a>
%H A305617 Bhabesh Das and Helen K. Saikia, <a href="https://vpcollege.org/wp-content/uploads/ijnt/volume_1/1.pdf">Identities for Near and Deficient Hyperperfect Numbers</a>, Indian Journal in Number Theory, Vol. 3 (2016), pp. 124-134.
%e A305617 35 is in the sequence since sigma(35) = 48 and 3*35/2 + 1/2 - 48 = 5 is a proper divisor of 35.
%t A305617 aQ[n_] := Module[{d = 3n/2+1/2-DivisorSigma[1,n]}, d>0 && d!=n && IntegerQ[d] && Divisible[n,d]]; Select[Range[2,1000000], aQ]
%o A305617 (PARI) isok(n) = (n % 2) && (k = (3*n+1)/2 - sigma(n)) && (k > 0) && !(n % k) && (k != n); \\ _Michel Marcus_, Jun 07 2018, corrected by _Amiram Eldar_, Dec 23 2024
%Y A305617 Cf. A000203, A000244, A007593, A271816, A305616.
%K A305617 nonn
%O A305617 1,1
%A A305617 _Amiram Eldar_, Jun 06 2018