A263876 - OEIS

%I #19 Dec 01 2019 07:16:05

%S 7,18,38,41,68,70,182,239,500,682,776,800,1068,1710,1744,4030,4060,

%T 5604,5744,8119,12156,15006,16610,17684,21490,25294,26884,27590,32060,

%U 32150,37416,37520,45630,47321,58724,71264,84906,88526,98864,109054,109610,128766

%N Numbers n such that n^2 + 1 has two distinct prime divisors less than n.

%C Subsequence of A256011.

%C The numbers n such that n^2 + 1 = p*q are semiprimes (A085722) are not in the sequence. According to this property, the corresponding sequence of the number of prime divisors with multiplicity is 3, 3, 3, 3, 4, 3, 5, 5, 3, 5, 3, 3, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, ...

%H Amiram Eldar, <a href="/A263876/b263876.txt">Table of n, a(n) for n = 1..500</a>

%e 7 is in the sequence because 7^2 + 1 = 2*5^2 => 2 and 5 are less than 7.

%t Select[Range[150000], PrimeNu[#^2+1] == 2&&FactorInteger[#^2+1][[1,1]]<# &&FactorInteger[#^2+1][[2,1]]<#&]

%o (PARI) for(n=1, 1e5, t=n^2+1; if ((omega(t) == 2) && (factor(t)[, 1][2] < n), print1(n, ", "))); \\ _Altug Alkan_, Oct 28 2015

%Y Cf. A085722, A144255, A256011, A263877.

%K nonn

%O 1,1

%A _Michel Lagneau_, Oct 28 2015