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A293391
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Integers n such that sigma(n)/phi(n) is a perfect square.
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5
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1, 14, 30, 105, 248, 264, 418, 714, 1485, 3080, 3135, 3596, 3828, 3956, 4064, 5396, 6678, 8636, 10098, 12648, 20026, 20790, 21318, 22152, 23374, 24882, 25714, 26040, 35074, 35343, 39105, 41656, 43890, 44660, 49938, 55154, 56134, 56536, 61344, 71145, 74613, 86304, 87087, 94944
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OFFSET
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1,2
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COMMENTS
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If x and y are coprime members of the sequence, then x*y is in the sequence.
Contains all members of A133028 except 3. (End)
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LINKS
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FORMULA
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a(n) = sigma(n)/phi(n) = m^2, for some integer m.
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EXAMPLE
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sigma(14)=3*8=24, phi(14)=14*(1/2)*(6/7)=6, sigma(14)/phi(14)=2^2, so 14 is in the list.
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MAPLE
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for n from 1 to 100000 do
r := numtheory[sigma](n)/numtheory[phi](n) ;
if issqr(r) then
printf("%d, ", n) ;
end if;
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MATHEMATICA
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Select[Range[10^5], IntegerQ@ Sqrt[DivisorSigma[1, #]/EulerPhi[#]] &] (* Michael De Vlieger, Dec 08 2017 *)
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PROG
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(PARI) isok(n) = my(q=sigma(n)/eulerphi(n)); issquare(q) && (denominator(q) == 1); \\ Michel Marcus, Dec 07 2017; corrected Sep 21 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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