OFFSET
1,1
COMMENTS
Also composite squarefree numbers n such that (3*p(i) - 1) | (3*n + 1).
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..65 (terms < 2*10^12)
EXAMPLE
The prime factors of 1045 are 5, 11 and 19. We see that (1045 + 1/3)/(5 - 1/3) = 224, (1045 + 1/3)/(11 - 1/3) = 98 and (1045 + 1/3)/(19 - 1/3) = 56. Hence 1045 is in the sequence.
The prime factors of 1639605 are 3, 5, 11, 19 and 523. We see that (1639605 + 1/3)/(3 - 1/3) = 614852, (1639605 + 1/3)/(5 - 1/3) = 351344, (1639605 + 1/3)/(11 - 1/3) = 153713, (1639605 + 1/3)/(19 - 1/3) = 87836 and (1639605 + 1/3)/(523 - 1/3) = 3137. Hence 1639605 is in the sequence.
The prime factors of 1117965 are 3, 5 and 74531. We see that (1117965 + 1/3)/(3 - 1/3) = 419237, (1117965 + 1/3)/(5 - 1/3) = 239564 but (1117965 + 1/3)/(74531 - 1/3) = 419237/27949. Hence 1117965 is not in the sequence.
MAPLE
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Paolo P. Lava, May 27 2013
EXTENSIONS
a(6)-a(23) from Giovanni Resta, Jun 02 2013
STATUS
approved