OFFSET
1,1
COMMENTS
A few years ago, challenges had been launched to find a prime power p^n, n>1 as large as possible, cf. links. I have remarked that it is easy to find arbitrarily large examples by taking the square of very large primes, rather than high powers of smaller primes, and suggested a merit function to take into account and penalize such "trivial" solutions. This led to a new challenge including the condition n > p. This sequence lists such numbers with the last condition relaxed to n >= p, which is sufficient to make the search nontrivial but includes a few more terms, namely the zeroless powers p^p (A051674 intersect A052382).
Possibly is a(80) = 19^44 the largest term; there are no greater ones in the first 500000 terms of A257278. - Reinhard Zumkeller, May 01 2015
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..80
S. S. Gupta, Can you find?, CYF n° 410 (Jan. 26, 2010) and CYF n° 412 (Nov. 13, 2012).
C. Rivera, Puzzle 607. A zeroless Prime power, primepuzzles.net, 2011
PROG
(PARI) is(n)=vecmin(digits(n)) && isprimepower(n, &n)>=n
(PARI) L=List(); lim=10; forprime(p=1, lim, for(n=p, lim*log(lim)\log(p), listput(L, p^n))); listsort(select(n->vecmin(digits(n)), L));
(Haskell)
a257279 n = a257279_list !! (n-1)
a257279_list = filter ((== 1) . a168046) a257278_list
-- Reinhard Zumkeller, May 01 2015
CROSSREFS
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Apr 28 2015
STATUS
approved