OFFSET
1,1
COMMENTS
Also composite squarefree numbers n such that (3p - 1) | (3n - 1).
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..68 (terms < 2*10^12)
EXAMPLE
The prime factors of 1445995 are 5, 19, 31 and 491. We see that (1445995 - 1/3)/(5 - 1/3) = 309856, (1445995 - 1/3)/(19 - 1/3) = 77464, (1445995 - 1/3)/(31 - 1/3) = 47152 and (1445995 - 1/3)/(491 - 1/3) = 2947. Hence 1445995 is in the sequence.
The prime factors of 1112307 are 3, 7 and 52967. We see that (1112307 - 1/3)/(3 - 1/3) = 417115, (1112307 - 1/3)/(7 - 1/3) = 166846 but (1112307 - 1/3)/(52967 - 1/3) = 166846/7945. Hence 1112307 is not in the sequence.
MAPLE
with(numtheory); ListA226364:=proc(i, j) local c, d, n, ok, p;
for n from 2 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1;
for d from 1 to nops(p) do if p[d][2]>1 or not type((n-j)/(p[d][1]-j), integer) then ok:=0; break; fi; od;
if ok=1 then print(n); fi; fi; od; end: ListA226364(10^9, 1/3);
PROG
(PARI) is(n, P)=n=3*n-1; for(i=1, #P, if(n%(3*P[i]-1), return(0))); 1
list(lim, P=[], n=1, mx=lim\2)=my(v=[], t); if(#P>1&&is(n, P), v=[n]); P=concat(P, 0); forprime(p=2, min(lim, mx), P[#P]=p; t=list(lim\p, P, n*p, p-1); if(#t, v=concat(v, t))); v \\ Charles R Greathouse IV, Jun 07 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Jun 05 2013
EXTENSIONS
a(5)-a(23) from Giovanni Resta, Jun 07 2013
STATUS
approved