A293391 Integers n such that sigma(n)/phi(n) is a perfect square.

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

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 and C. Leibovici, Why is this sequence 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

(PARI) 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