A076444 Smallest powerful number (definition 1) such that a(n)+n is also powerful.

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

Donovan Johnson, Table of n, a(n) for n = 1..109

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

Cf. A001694, A103952, A103953, A103954.

Sequence in context: A132586 A208400 A103953 * A023056 A103954 A217012

Adjacent sequences: A076441 A076442 A076443 * A076445 A076446 A076447

Keyword

nonn

Author

Jud McCranie, Oct 13 2002

Extensions

More terms from Max Alekseyev, Feb 22 2005

Status

approved