A283449 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.

870, 378, 107827277891825604, 178101, 594839010, 275223438741, 26584448904822018, 40373802, 420707243066850, 952809806744100

Offset

2,1

Comments

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

Links

Table of n, a(n) for n=2..11.

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

Example

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.

Prog

(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)))))

Crossrefs

Cf. A058041, A257659.

Sequence in context: A205224 A165385 A165377 * A351878 A158669 A206172

Adjacent sequences: A283446 A283447 A283448 * A283450 A283451 A283452

Keyword

nonn,hard,more

Author

Felix Fröhlich, Mar 07 2017

Extensions

a(11) from Giovanni Resta, Mar 09 2017

Status

approved