

A056828


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


3




OFFSET

1,1


COMMENTS

Mollin and Walsh conjectured that there are no further terms.
HeathBrown proved that the sequence is finite.
No other terms less than 40000000.  Paul.Jobling(AT)WhiteCross.com, May 14 2001


REFERENCES

HeathBrown, D. R. "Ternary Quadratic Forms and Sums of Three SquareFull Numbers." In Seminaire de Theorie des Nombres, Paris 198687 (Ed. C. Goldstein). Boston, MA: Birkhauser, pp. 137163, 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, 9:801806, 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.
Sequence in context: A194400 A177768 A243582 * A113505 A184920 A076796
Adjacent sequences: A056825 A056826 A056827 * A056829 A056830 A056831


KEYWORD

fini,nonn


AUTHOR

Henry Bottomley, Aug 30 2000


STATUS

approved



