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 A293391 Integers n such that sigma(n)/phi(n) is a perfect square. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From Robert Israel, Dec 12 2017: (Start) Intersection of A011257 and A020492. 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) LINKS Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 349 terms from Robert Israel) J. A. B. Dris, C. Leibovici, Why is this sequences not in the OEIS?, October 8 2017. ProofWiki, Integers whose ratio between sigma and phi is square, misses the second term, 14 as of Dec 2017. FORMULA a(n) = sigma(n)/phi(n) = m^2, for some integer m. EXAMPLE 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. MAPLE for n from 1 to 100000 do     r := numtheory[sigma](n)/numtheory[phi](n) ;     if issqr(r) then         printf("%d, ", n) ;     end if; end do: # R. J. Mathar, Dec 07 2017 MATHEMATICA Select[Range[10^5], IntegerQ@ Sqrt[DivisorSigma[1, #]/EulerPhi[#]] &] (* Michael De Vlieger, Dec 08 2017 *) PROG isok(n) = my(q=sigma(n)/eulerphi(n)); issquare(q) && (denominator(q) == 1); \\ Michel Marcus, Dec 07 2017; corrected Sep 21 2019 CROSSREFS Cf. A000010, A000203, A011257, A020492, A133028, A289336, A289412, A292422. Sequence in context: A101960 A075208 A228124 * A015222 A054103 A344397 Adjacent sequences:  A293388 A293389 A293390 * A293392 A293393 A293394 KEYWORD nonn AUTHOR Jose Arnaldo Bebita Dris, Oct 08 2017 STATUS approved

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Last modified June 15 22:06 EDT 2021. Contains 345053 sequences. (Running on oeis4.)