OFFSET
1,1
COMMENTS
All known terms have only two prime factors, one slightly larger than the other.
a(435) = 7523021437 = 1597 * 1933 * 2437 is the first term which has more than two prime factors. - Hiroaki Yamanouchi, Sep 28 2015
a(5586) > 10^12. - Hiroaki Yamanouchi, Sep 28 2015
LINKS
Hiroaki Yamanouchi, Table of n, a(n) for n = 1..5885
EXAMPLE
a(1) = 777923 because this is the first squarefree composite number n such that exactly seven integers b except 0 exist such that for every prime factor p of n, p+b divides n+b (-879, -878, -875, -872, -867, -863, -839): 777923=881*883 and 2, 4 both divide 777044 and 3, 5 both divide 777045 and 6, 8 both divide 777048 and 9, 11 both divide 777051 and 14, 16 both divide 777056 and 18, 20 both divide 777060 and 42, 44 both divide 777084.
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==7, print1(n, ", ")))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Tim Johannes Ohrtmann, May 12 2015
EXTENSIONS
a(16)-a(27) from Hiroaki Yamanouchi, Sep 26 2015
STATUS
approved