A067811 Numbers n such that phi(n)^2 + sigma(n)^2 is an integer square.

7, 32, 33, 41, 68, 145, 209, 237, 239, 266, 328, 372, 384, 385, 442, 522, 622, 905, 945, 1157, 1243, 1288, 1357, 1581, 1615, 1643, 1798, 1853, 1885, 1978, 1995, 2093, 2418, 2541, 2698, 2765, 2769, 2981, 3013, 3161, 3315, 3451, 3519, 3577, 4041, 4309, 4318

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

phi(32)^2 + sigma(32)^2 = 16^2 + 63^2 = 4225 = 65^2, so 32 is a term of the sequence.

Mathematica

Select[Range[10^4], IntegerQ[Sqrt[EulerPhi[ # ]^2 + DivisorSigma[1, # ]^2]] &]

Prog

(PARI) isok(n) = issquare(eulerphi(n)^2+sigma(n)^2); \\ Michel Marcus, Aug 13 2019

Crossrefs

Cf. A000010, A000203.

Sequence in context: A214490 A360261 A164819 * A044084 A044465 A029484

Adjacent sequences: A067808 A067809 A067810 * A067812 A067813 A067814

Keyword

easy,nonn

Author

Joseph L. Pe, Feb 07 2002

Status

approved