A067268 Numbers k such that k and k^2+1 have the same number of distinct prime factors.

2, 4, 12, 15, 16, 18, 22, 28, 34, 35, 38, 39, 44, 45, 46, 48, 50, 51, 52, 58, 62, 65, 68, 69, 76, 80, 82, 85, 86, 88, 92, 95, 96, 100, 104, 105, 106, 108, 118, 132, 136, 138, 141, 144, 145, 152, 158, 159, 164, 166, 171, 174, 175, 178, 188, 194, 196, 201, 202, 205

Offset

1,1

Links

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

Formula

Numbers k such that omega(k) = omega(k^2+1).

Example

2 is a term since omega(2) = omega(2^2+1) = 1.

Mathematica

Select[Range[250], PrimeNu[#]==PrimeNu[#^2+1]&] (* Harvey P. Dale, Feb 07 2019 *)

Prog

(Magma) [k:k in [1.. 210 ]| #PrimeDivisors(k) eq #PrimeDivisors(k^2+1)]; // Marius A. Burtea, Feb 18 2020

Crossrefs

Cf. A001221, A002522, A128428, A272044.

Sequence in context: A297064 A263466 A106135 * A285378 A082458 A230770

Adjacent sequences: A067265 A067266 A067267 * A067269 A067270 A067271

Keyword

easy,nonn

Author

Benoit Cloitre, Feb 21 2002

Status

approved