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A248742 Numbers of the form x^2+1 with at most two prime factors. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 7 16:00 EDT 2021. Contains 343652 sequences. (Running on oeis4.)