A066764 Numbers k such that (k, sigma(k)) lies on a circle with integral radius centered at the origin, i.e., k^2 + sigma(k)^2 is a square.

3, 8, 30, 140, 315, 319, 460, 840, 864, 936, 1040, 1287, 1836, 2480, 2600, 6076, 6200, 7788, 11398, 12035, 12415, 12584, 13260, 13734, 15886, 18480, 26078, 33820, 40640, 42665, 46200, 55860, 68352, 70266, 70645, 75330, 78939, 81740, 98230

Offset

1,1

Comments

Also numbers such that A017665(k)^2 + A017666(k)^2 is a square. - Michel Marcus, May 23 2015

Links

Harry J. Smith, Table of n, a(n) for n = 1..731

Example

3^2 + sigma(3)^2 = 9 + 16 = 5^2; so 3 is a term of the sequence.

Mathematica

Select[ Range[ 1, 10^5 ], IntegerQ[ Sqrt[ #^2 + DivisorSigma[ 1, # ]^2 ] ] & ]

Prog

(PARI) isok(k) = { issquare(k^2 + sigma(k)^2) } \\ Harry J. Smith, Mar 24 2010

Crossrefs

Cf. A017665, A017666, A066763.

Sequence in context: A161779 A074501 A009123 * A349426 A059171 A261766

Adjacent sequences: A066761 A066762 A066763 * A066765 A066766 A066767

Keyword

nonn,changed

Author

Joseph L. Pe, Jan 17 2002

Status

approved