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

Author

Jud McCranie, Oct 13 2002

Keywords

• nonn

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

Examples

			214369=463^2 and 214375=5^4*7^3 are the smallest pair of powerful numbers differing by 6, so a(6)=214369.
		

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

Crossrefs

Cf. A001694, A103952, A103953, A103954.

Extensions

More terms from Max Alekseyev, Feb 22 2005