A056828 Numbers that are not the sum of at most three powerful (1) numbers.

7, 15, 23, 87, 111, 119

Offset: 1

Author

Henry Bottomley, Aug 30 2000

Keywords

• fini
• nonn

Comments

Mollin and Walsh conjectured that there are no further terms.

Heath-Brown proved that the sequence is finite.

No other terms less than 40000000. - Paul.Jobling(AT)WhiteCross.com, May 14 2001

Examples

			Smallest powerful numbers are 1, 4, 8, 9, 16, 25,... so 7, 15 and 23 are not the sum of one, two or three of them.
		

References

• D. R. Heath-Brown, "Ternary Quadratic Forms and Sums of Three Square-Full Numbers." In Séminaire de Théorie des Nombres, Paris 1986-87 (Ed. C. Goldstein). Boston, MA: Birkhauser, pp. 137-163, 1988.

Links

• R. A. Mollin and P. G. Walsh, On Powerful Numbers, Intern. J. Math. and Math. Sci, 9:801-806, 1986.
• Eric Weisstein's World of Mathematics, Powerful Number.

Crossrefs

Cf. A001694, A076871, A113505.