A305617 Deficient 2-hyperperfect numbers: numbers k such that 3*k/2 + 1/2 - sigma(k) is a proper divisor of k.
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
Keywords
Examples
35 is in the sequence since sigma(35) = 48 and 3*35/2 + 1/2 - 48 = 5 is a proper divisor of 35.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..74
- Bhabesh Das and Helen K. Saikia, Identities for Near and Deficient Hyperperfect Numbers, Indian Journal in Number Theory, Vol. 3 (2016), pp. 124-134.
Programs
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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] -
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
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