OFFSET
1,2
COMMENTS
The sequence contains exactly 33 terms.
EXAMPLE
By the condition, a(12) should be more than a(11)=191. Since 12 has vector of positive exponents (2,1), then we seek already constructed prime terms p<q in the sequence and choose the smallest number of the form p^2*q>191. It is 275=5^2*11. Thus a(12)=275. Further, a(13) should be the nearest prime more than 275. It is 277.
PROG
(Sage)
@CachedFunction
def A178443(n):
if n <= 2: return {1:1, 2:3}[n]
if is_prime(n): return next_prime(A178443(n-1))
psig_n = list(m for p, m in factor(n))
primes_seen = sorted(set(filter(is_prime, map(A178443, range(2, n)))))
possibles = (prod(p**m for p, m in zip(pvec, psig_n)) for pvec in Combinations(primes_seen, len(psig_n)))
return min(p for p in possibles if p > A178443(n-1))
# D. S. McNeil, Jan 01 2011
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Vladimir Shevelev, Dec 22 2010
STATUS
approved