A248742 Numbers of the form x^2+1 with at most two prime factors.

2, 5, 10, 17, 26, 37, 65, 82, 101, 122, 145, 197, 226, 257, 362, 401, 485, 577, 626, 677, 785, 842, 901, 1157, 1226, 1297, 1522, 1601, 1765, 1937, 2026, 2117, 2305, 2402, 2501, 2602, 2705, 2917, 3137, 3365, 3482, 3601, 3722, 3845, 4097, 4226, 4357, 4762

Offset: 1

Author

R. J. Mathar, Oct 13 2014

Keywords

• nonn

Comments

Prime factors are counted with multiplicity, as in A144255.

Iwaniec shows that the sequence is infinite.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• H. Iwaniec, Almost-primes represented by quadratic polynomials, Inventiones Mathematicae 47:2 (1978), pp. 171-188.
• Vishaal Kapoor, Almost-primes represented by quadratic polynomials, MS thesis (2006). arXiv:1910.02885 [math.NT]
• Robert J. Lemke Oliver, Almost-primes represented by quadratic polynomials, Acta Arithm. 151 (2012) 241. DOI: 10.4064/aa151-3-2
• Wikipedia, Landau's problems

Crossrefs

Cf. A002496, A069987.

Programs

PARI

is(n)=issquare(n-1) && bigomega(n)<3 \\ Charles R Greathouse IV, Feb 05 2017

Formula

A002496 UNION A144255.