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

7, 15, 23, 87, 111, 119

Offset

1,1

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

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

Table of n, a(n) for n=1..6.

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.

Example

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.

Crossrefs

Cf. A001694, A076871, A113505.

Sequence in context: A177768 A243582 A336819 * A113505 A184920 A076796

Adjacent sequences: A056825 A056826 A056827 * A056829 A056830 A056831

Keyword

fini,nonn

Author

Henry Bottomley, Aug 30 2000

Status

approved