OFFSET
1,1
COMMENTS
All known terms have only two prime factors whereby the second prime factor is only slightly larger than the first.
a(3384) > 10^12. - Hiroaki Yamanouchi, Sep 26 2015
LINKS
Hiroaki Yamanouchi, Table of n, a(n) for n = 1..3383
EXAMPLE
a(1) = 182293 because this is the first squarefree composite number n such that exactly eight integers except 0 exist such that for every prime factor p of n applies that p+b divides n+b (-419, -418, -413, -412, -405, -403, -373, -349): 182293=421*433 and 2, 14 both divide 181874 and 3, 15 both divide 181875 and 8, 20 both divide 181880 and 9, 21 both divide 181881 and 16, 28 both divide 181888 and 18, 30 both divide 181890 and 48, 60 both divide 181920 and 72, 84 both divide 181944.
PROG
(PARI) for(n=2, 1000000, if(!isprime(n), if(issquarefree(n), f=factor(n); k=0; for(b=-(f[1, 1]-1), n, c=0; for(i=1, #f[, 1], if((n+b)%(f[i, 1]+b)>0, c++)); if(c==0, if(!b==0, k++))); if(k==8, print1(n, ", ")))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Tim Johannes Ohrtmann, Jun 12 2015
EXTENSIONS
a(4)-a(25) from Hiroaki Yamanouchi, Sep 26 2015
STATUS
approved