2,1

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

J. M. DeKoninck and F. Luca,Partial Sums of Powers of Prime Factors,Journal of Integer Sequences, 10 (2007), Article 07.1.6.

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.

(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)))))

Cf.A058041,A257659.

Sequence in context:A205224A165385A165377*A351878A158669A206172

Adjacent sequences:A283446A283447A283448*A283450A283451A283452

nonn,hard,more

Felix Fröhlich,Mar 07 2017

a(11) fromGiovanni Resta,Mar 09 2017

approved