A272078 Numbers k such that k^2 + 1 is product of 3 distinct primes.

13, 17, 21, 23, 27, 31, 33, 37, 53, 55, 63, 67, 72, 75, 77, 81, 87, 89, 91, 97, 98, 103, 105, 109, 111, 112, 113, 115, 119, 122, 125, 127, 128, 129, 135, 137, 138, 142, 147, 148, 149, 151, 153, 155, 161, 162, 163, 167, 172, 174, 179, 185, 189, 192, 197, 200, 208

Offset: 1

Author

K. D. Bajpai, Apr 19 2016

Keywords

• nonn

Examples

			13 appears in the list because 13^2 + 1 = 170 = 2 * 5 * 17.
21 appears in the list because 21^2 + 1 = 442 = 2 * 13 * 17.
		

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007304, A046386, A176686, A176687.

Programs

Mathematica

A272078 = {}; Do[ k = Last /@ FactorInteger[n^2 + 1]; If[k == {1, 1, 1}, AppendTo[A272078, n]], {n, 1000}]; A272078
Select[Range[1000], Last /@ FactorInteger[#^2 + 1] == {1, 1, 1} &]

PARI

isok(k) = my(x=k^2+1); (omega(x)==3) && (bigomega(x)==3); \\ Michel Marcus, Mar 11 2020