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

1,1

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

Formula

A002496 UNION A144255.

Prog

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

Crossrefs

Cf. A002496, A069987.

Sequence in context: A300164 A248193 A069987 * A246884 A119114 A062493

Adjacent sequences: A248739 A248740 A248741 * A248743 A248744 A248745

Keyword

nonn

Author

R. J. Mathar, Oct 13 2014

Status

approved