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A283449
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Smallest composite that is not an n-th power, but can be written as the sum of the n-th powers of two or more of its distinct prime factors.
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0
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OFFSET
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2,1
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COMMENTS
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a(2)-a(10) are given at the bottom of page 7 of DeKoninck, Luca, 2007.
a(12) <= 2183128876699456840262188163473698588738, a(13)=26036721925607706907290, and a(14)=297558232681902995490. Giovanni Resta, Mar 09 2017
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LINKS
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EXAMPLE
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For n = 2: 870 = 2 * 3 * 5 * 29 and 2^2 + 5^2 + 29^2 = 870. Since 870 is the smallest number that is not a square and can be written as the sum of squares of some of its distinct prime factors, a(2) = 870.
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PROG
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(PARI) nextrowcomb(rowarr) = my(k=#rowarr, i=0); while(rowarr[k]==1, rowarr[k]=0; i++; k--); while(rowarr[k]==0 && k > 1, k--); if(rowarr[k]==1, rowarr[k]=0; rowarr[k+1]=1; k=k+2; while(i > 0, rowarr[k]=1; k++; i--), for(x=k, k+i, rowarr[x]=1)); rowarr
a(n) = forcomposite(c=1, , if(!ispower(c, n), my(f=factor(c)[, 1]~, v=vector(#f)); while(1, my(s=0); for(k=1, #v, if(v[k]==1, s=s+f[k]^n)); if(s==c, return(c)); if(vecmin(v)==1, break, v=nextrowcomb(v)))))
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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