A263877 Numbers n such that n^2 + 1 has three distinct prime divisors less than n.

21, 43, 57, 72, 99, 111, 117, 119, 128, 132, 142, 172, 174, 185, 192, 193, 200, 211, 212, 216, 251, 268, 294, 305, 322, 336, 338, 342, 351, 360, 378, 394, 408, 418, 431, 443, 448, 450, 460, 485, 498, 509, 515, 524, 552, 560, 562, 568, 580, 601, 606, 612, 616

Offset

1,1

Comments

Subsequence of A256011.

The "triprimes n^2+1 numbers" are the numbers that are the product of exactly three (not necessarily distinct) primes less than n.

If the three prime divisors are distinct, the corresponding subsequence is 21, 72, 111, 119, 128, 142, 172, 174, 185, 192, 200, 211, 212, 216, 294, 305, 322, 336, 338, 342, 351, 360, 394, 431, 448, 450, 460, 485, 498, 509, 524, 552, 560, 562, 580, ...

The corresponding sequence of the number of prime divisors with multiplicity is 3, 4, 5, 3, 4, 3, 4, 3, 3, 4, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 4, 5, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 4, 3, 6, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 5, 3, 3, 4, 3, 4, 3, 3, 3, 3, 4, 3, 4, ...

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

72 is in the sequence because 72^2 + 1 = 5*17*61 and 5, 17 and 61 are less than 72.

Mathematica

Select[Range[800], PrimeNu[#^2+1] == 3&&FactorInteger[#^2+1][[1, 1]]<#&& FactorInteger[#^2+1][[2, 1]]<#&&FactorInteger[#^2+1][[3, 1]]<#&]

Prog

(PARI) for(n=1, 1e3, t=n^2+1; if ((omega(t) == 3) && (factor(t)[, 1][3] < n), print1(n, ", "))); \\ Altug Alkan, Oct 28 2015

Crossrefs

Cf. A014612, A256011, A263876.

Sequence in context: A043167 A043947 A335477 * A041870 A041868 A135391

Adjacent sequences: A263874 A263875 A263876 * A263878 A263879 A263880

Keyword

nonn

Author

Michel Lagneau, Oct 28 2015

Status

approved