A114078 Numbers k such that phi(k)*sigma(k) is a fourth power.

1, 170, 595, 714, 121056, 480441, 529620, 706063, 706237, 729752, 755972, 815654, 2162808, 2449062, 2827789, 2927848, 2957416, 2994681, 2995419, 3010227, 3019028, 3019772, 3080140, 3093860, 3103464, 3206364, 3213804

Offset

1,2

References

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 170, p. 54, Ellipses, Paris 2008.

Links

Amiram Eldar, Table of n, a(n) for n = 1..600

Example

phi(595) * sigma(595) = 331776 = 24^4.

Mathematica

Select[Range[3300000], IntegerQ[Power[EulerPhi[#] DivisorSigma[1, #], (4)^-1]]&]  (* Harvey P. Dale, Mar 14 2011 *)

Prog

(PARI) isok(n) = ispower(eulerphi(n)*sigma(n), 4); \\ Michel Marcus, Jan 09 2014
(Magma) [k:k in [1..3300000]| IsPower(EulerPhi(k)*DivisorSigma(1, k), 4)]; // Marius A. Burtea, Sep 19 2019

Crossrefs

Cf. A062354, subsequence of A011257.

Sequence in context: A364905 A362561 A045089 * A031704 A173275 A301867

Adjacent sequences: A114075 A114076 A114077 * A114079 A114080 A114081

Keyword

nonn

Author

Giovanni Resta, Feb 13 2006

Status

approved