OFFSET
1,1
COMMENTS
Within the range of the data, a(n)^2 = A340642(n), i.e., no 3 immediately consecutive perfect powers x^p1, y^p2, z^p3 with min (p1, p2, p3) > 2 are seen. Is there a counterexample?
LINKS
David A. Corneth, Table of n, a(n) for n = 1..611 (first 181 terms from Hugo Pfoertner)
PROG
(PARI) a340643(limit)={my(p2=999, p1=2, n2=1, n1=4); for(n=5, limit, my(p0=ispower(n)); if(p0>1, if(issquare(n1)&p2>2&p0>2, print1(sqrtint(n1), ", ")); n2=n1; n1=n; p2=p1; p1=p0))};
a340643(10^8)
(PARI) upto(n) = {n *= n; my(v = List(), res = List([2])); for(i = 2, sqrtnint(n, 3), for(e = 3, logint(n, i), listput(v, i^e) ); ); listsort(v, 1); for(i = 1, #v - 1, if(sqrtint(v[i]) + 1 == sqrtint(v[i+1]) - issquare(v[i+1]), listput(res, sqrtint(v[i+1]-issquare(v[i+1]))); ) ); res }
CROSSREFS
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Jan 14 2021
EXTENSIONS
More terms from David A. Corneth, Jan 14 2021
STATUS
approved