

A178443


Two numbers k and l we call equivalent if they have the same vector of exponents with positive components in prime power factorization. Let a(1)=1, a(2)=3. If n>=3 is prime, then a(n) is the smallest prime greater than a(n1); otherwise, a(n)>a(n1) is the smallest number equivalent to n such that prime power factorization of a(n) contains only primes which already appeared in the sequence.


1



1, 3, 5, 9, 11, 15, 17, 27, 121, 187, 191, 275, 277, 573, 831, 14641, 14653, 109443, 109451, 131877, 161183, 249101, 249103, 254221, 214710409, 1603785503, 3146151623077, 23500268975459, 23500268975497, 352504034632455, 352504034632459, 675511501766876508493, 8283939628810696270871857123
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OFFSET

1,2


COMMENTS

The sequence contains exactly 33 terms.


LINKS

Table of n, a(n) for n=1..33.


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(n1))
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(n1))
# [D. S. McNeil, Jan 01 2011]


CROSSREFS

Cf. A178442, A172980, A172999
Sequence in context: A064988 A166699 A191110 * A287421 A214214 A281505
Adjacent sequences: A178440 A178441 A178442 * A178444 A178445 A178446


KEYWORD

nonn,fini,full


AUTHOR

Vladimir Shevelev, Dec 22 2010


STATUS

approved



