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

1,1

Links

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

Example

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.

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} &]

Prog

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

Crossrefs

Cf. A007304, A046386, A176686, A176687.

Sequence in context: A108560 A274422 A134257 * A205722 A105731 A060343

Adjacent sequences: A272075 A272076 A272077 * A272079 A272080 A272081

Keyword

nonn

Author

K. D. Bajpai, Apr 19 2016

Status

approved