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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Oct 28 2015
STATUS
approved