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URL: https://oeis.org/A305617

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A305617
Deficient 2-hyperperfect numbers: numbers k such that 3*k/2 + 1/2 - sigma(k) is a proper divisor of k.
2
3, 9, 27, 35, 39, 55, 81, 243, 279, 387, 715, 729, 1443, 2187, 2619, 3655, 5635, 6561, 10855, 12635, 19683, 59049, 77283, 177147, 178119, 294759, 443135, 531441, 817167, 1170723, 1594323, 1605987, 1632231, 1710963, 1947159, 2410239, 2624375, 2655747, 3944255
OFFSET
1,1
COMMENTS
Includes all the powers of 3 (A000244).
A combination of the notions 2-hyperperfect numbers (A007593) and deficient-perfect numbers (A271816).
LINKS
Bhabesh Das and Helen K. Saikia, Identities for Near and Deficient Hyperperfect Numbers, Indian Journal in Number Theory, Vol. 3 (2016), pp. 124-134.
EXAMPLE
35 is in the sequence since sigma(35) = 48 and 3*35/2 + 1/2 - 48 = 5 is a proper divisor of 35.
MATHEMATICA
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]
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jun 06 2018
STATUS
approved