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A063274
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Number of powerful numbers (definition 1) required to sum to n.
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7
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1, 2, 3, 1, 2, 3, 4, 1, 1, 2, 3, 2, 2, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 1, 2, 1, 2, 2, 3, 2, 1, 2, 2, 2, 1, 2, 3, 3, 2, 2, 3, 2, 2, 2, 3, 3, 2, 1, 2, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 3, 2, 1, 2, 3, 3, 2, 3, 3, 3, 1, 2, 2, 3, 2, 3, 3, 3, 2, 1, 2, 3, 3, 2, 3, 4, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 1, 2, 3, 3, 2, 3
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OFFSET
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1,2
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COMMENTS
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Heath-Brown proves that a(n) <= 3 for all large n. It seems that n > 119 suffices. - Charles R Greathouse IV, Nov 19 2012
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REFERENCES
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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.
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LINKS
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EXAMPLE
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The powerful numbers (A001694) start 1,4,8,9,... 11=1+1+9 and is not the sum of fewer terms, so a(11)=3.
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PROG
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(PARI) W=vector(99); W[1]=1; for(n=2, #W, if(ispowerful(n), W[n]=1; next); b=n; for(i=1, n\2, b=min(b, W[i]+W[n-i])); W[n]=b); W \\ Charles R Greathouse IV, Nov 19 2012
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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