A066134 Numbers from A066112 that are neither square nor twice a square, i.e., are not in A028982 but are in A028983.
48, 180, 245, 432, 500, 605, 931, 980, 1200, 1280, 1620, 1805, 2205, 2352, 2420, 3380, 3724, 3888, 3920, 4500, 4655, 5445, 5780, 5808, 6125, 6845, 7203, 7220, 7936, 8112, 8379, 8405, 8820, 9072, 9251, 9680, 10580, 10800, 11520, 11760, 12500
Offset: 1
Keywords
Examples
180 is neither square nor twice a square, but sigma_4(180)/sigma_2(180) = 1135275414/49686 = 22849 = 73*313.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)
Programs
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Mathematica
q[k_] := !IntegerQ[Sqrt[k]] && !IntegerQ[Sqrt[k/2]] && IntegerQ[r = DivisorSigma[4, k]/DivisorSigma[2, k]] && !PrimeQ[r]; Select[Range[12500], q] (* Amiram Eldar, Feb 23 2025 *)
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PARI
{ n=0; for (m=1, 10^9, if (issquare(m) || issquare(m/2), next); if (frac(f=sigma(m, 4)/sigma(m, 2)), next); if (!isprime(f), write("b066134.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Feb 02 2010