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A187054
Numbers that are not the sum of three powerful numbers (A001694).
0
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
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.
Sequence in context: A247865 A271505 A343915 * A135693 A135367 A141493
KEYWORD
nonn,fini,full
AUTHOR
STATUS
approved