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

%I A263877 #17 Nov 26 2019 04:17:53
%S A263877 21,43,57,72,99,111,117,119,128,132,142,172,174,185,192,193,200,211,
%T A263877 212,216,251,268,294,305,322,336,338,342,351,360,378,394,408,418,431,
%U A263877 443,448,450,460,485,498,509,515,524,552,560,562,568,580,601,606,612,616
%N A263877 Numbers n such that n^2 + 1 has three distinct prime divisors less than n.
%C A263877 Subsequence of A256011.
%C A263877 The "triprimes n^2+1 numbers" are the numbers that are the product of exactly three (not necessarily distinct) primes less than n.
%C A263877 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, ...
%C A263877 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, ...
%H A263877 Amiram Eldar, <a href="/A263877/b263877.txt">Table of n, a(n) for n = 1..10000</a>
%e A263877 72 is in the sequence because 72^2 + 1 = 5*17*61 and 5, 17 and 61 are less than 72.
%t A263877 Select[Range[800], PrimeNu[#^2+1] == 3&&FactorInteger[#^2+1][[1,1]]<#&& FactorInteger[#^2+1][[2,1]]<#&&FactorInteger[#^2+1][[3,1]]<#&]
%o A263877 (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
%Y A263877 Cf. A014612, A256011, A263876.
%K A263877 nonn
%O A263877 1,1
%A A263877 _Michel Lagneau_, Oct 28 2015