OFFSET
1,4
COMMENTS
Anti-factor is here defined as almost synonym with anti-divisor (except without the restriction of being less than n for anti-divisor.) ODD p^k is anti-factor (<n or >n) of n iff p^i, 1<=i<=k are anti-factors of n (note that this only applies to ODD anti-factors.)
In this sequence p < n, but p^k with k>=2 may be larger than n.
a(n) = 1 iff 2n-1 and 2n+1 are twin primes;
a(n) = 2n-1 iff 2n-1 is composite, 2n+1 is prime;
a(n) = 2n+1 iff 2n-1 is prime, 2n+1 is composite;
a(n) = (2n-1)(2n+1) iff 2n-1 and 2n+1 are both composite.
LINKS
Daniel Forgues, Table of n, a(n) for n=1..49999
FORMULA
a(n) = {product of odd prime factors < 2n-1 of 2n-1, with multiplicity} * {product of odd prime factors < 2n+1 of 2n+1, with multiplicity}
GCD(a(n), a(n+1)) = {product of odd prime factors < 2n+1 of 2n+1, with multiplicity} (cf. A171435)
EXAMPLE
3 is an anti-factor (and anti-divisor) of 5, and 3^2=9 is also an anti-factor (but not an anti-divisor since > 5) of 5.
CROSSREFS
KEYWORD
nonn
AUTHOR
Daniel Forgues, Dec 10 2009
STATUS
approved