A076090 a(1) = 1; for n > 1, smallest number > 1 which is the n-th power of the sum of its digits, or 0 if no such number exists.

1, 81, 512, 2401, 17210368, 34012224, 612220032, 20047612231936, 3904305912313344, 13744803133596058624, 8007313507497959524352, 2518170116818978404827136, 81920000000000000

Offset: 1

Author

Amarnath Murthy, Oct 07 2002

Keywords

• nonn
• base

Examples

			a(3) = 512 = 8^3 and no smaller number (>1) can have this property. (This has been established in the reference.)
		

References

• Amarnath Murthy, The largest and the smallest m-th power whose digits sum /product is its m-th root. To appear in Smarandache Notions Journal.
• Amarnath Murthy, e-book, " Ideas on Smarandache Notions " MS.LIT

Crossrefs

Cf. A046017.

Formula

For n > 1, a(n) = A046017(n)^n. - David Wasserman, Mar 25 2005

a(n)=A072408(n), n>1. [From R. J. Mathar, Sep 23 2008]

Extensions

More terms from David Wasserman, Mar 25 2005