A187054 Numbers that are not the sum of three powerful numbers (A001694).

1, 2, 4, 5, 7, 8, 15, 23, 31, 87, 111, 119

Offset

1,2

Comments

Heath-Brown shows that this sequence is finite, resolving a conjecture of Erdos. Presumably a(12) = 119 is the last term.

References

D. R. Heath-Brown, "Sums of three square-full numbers". Number theory, Vol. I (Budapest, 1987), pp. 163-171, Colloq. Math. Soc. János Bolyai, 51, North-Holland, Amsterdam, 1990.

D. R. Heath-Brown, "Ternary quadratic forms and sums of three square-full numbers". Séminaire de Théorie des Nombres, Paris 1986-87, pp. 137-163, Progr. Math., 75, Birkhäuser Boston, Boston, MA, 1988.

Links

Table of n, a(n) for n=1..12.

P. Erdos, Problems and results on number theoretic properties of consecutive integers and related questions, Proceedings of the Fifth Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1975), Congress. Numer. XVI (1976), pp. 25-44.

Mathematica

powerfulQ[n_] := n == 1 || Min[Last /@ FactorInteger[n]] > 1; nn = 1000; pow = Select[Range[nn], powerfulQ]; Complement[Range[nn], Select[Union[Flatten[Outer[Plus, pow, pow, pow]]], # <= nn &]] (* T. D. Noe, Mar 02 2011 *)

Crossrefs

Proper subsequence of A135367.

Cf. A076871, A135693.

Sequence in context: A247865 A271505 A343915 * A135693 A135367 A141493

Adjacent sequences: A187051 A187052 A187053 * A187055 A187056 A187057

Keyword

nonn,fini,full

Author

Charles R Greathouse IV, Mar 02 2011

Status

approved