login
A076444
Smallest powerful number (definition 1) such that a(n)+n is also powerful.
4
8, 25, 1, 4, 4, 214369, 1, 1, 16, 2187, 16, 4, 36, 30459361, 1, 9, 8, 9, 8, 16, 4, 27, 4, 1, 100, 1, 9, 4, 196, 6859, 1, 4, 16, 899236854927, 1, 36, 27, 1331, 25, 9, 8, 518436000625, 200, 64, 4, 243, 25, 1, 32, 625, 49, 144, 72, 27, 9, 8, 64, 109503, 49, 4, 64, 3025, 1, 8, 16
OFFSET
1,1
COMMENTS
McDaniel proved that a(n) exists for all n > 0.
Sister sequence of a(n)+n given by A103952.
a(110) > 10^22. - Donovan Johnson, Nov 19 2011
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, B16
LINKS
Wayne L. McDaniel, Representations of every integer as the difference of powerful numbers, Fibonacci Quarterly 20 (1982), pp. 85-87.
Eric Weisstein's World of Mathematics, Powerful numbers
EXAMPLE
214369=463^2 and 214375=5^4*7^3 are the smallest pair of powerful numbers differing by 6, so a(6)=214369.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jud McCranie, Oct 13 2002
EXTENSIONS
More terms from Max Alekseyev, Feb 22 2005
STATUS
approved