login
A263876
Numbers n such that n^2 + 1 has two distinct prime divisors less than n.
2
7, 18, 38, 41, 68, 70, 182, 239, 500, 682, 776, 800, 1068, 1710, 1744, 4030, 4060, 5604, 5744, 8119, 12156, 15006, 16610, 17684, 21490, 25294, 26884, 27590, 32060, 32150, 37416, 37520, 45630, 47321, 58724, 71264, 84906, 88526, 98864, 109054, 109610, 128766
OFFSET
1,1
COMMENTS
Subsequence of A256011.
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, ...
LINKS
EXAMPLE
7 is in the sequence because 7^2 + 1 = 2*5^2 => 2 and 5 are less than 7.
MATHEMATICA
Select[Range[150000], PrimeNu[#^2+1] == 2&&FactorInteger[#^2+1][[1, 1]]<# &&FactorInteger[#^2+1][[2, 1]]<#&]
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Oct 28 2015
STATUS
approved