A263876 Numbers n such that n^2 + 1 has two distinct prime divisors less than n.

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

Amiram Eldar, Table of n, a(n) for n = 1..500

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

Cf. A085722, A144255, A256011, A263877.

Sequence in context: A297646 A320281 A169677 * A192751 A272459 A133673

Adjacent sequences: A263873 A263874 A263875 * A263877 A263878 A263879

Keyword

nonn

Author

Michel Lagneau, Oct 28 2015

Status

approved