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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.)