A082872 a^n + b^n + c^n + ..., where a*b*c* ... is the prime factorization of n.

1, 4, 27, 32, 3125, 793, 823543, 768, 39366, 9766649, 285311670611, 539633, 302875106592253, 678223089233, 30531927032, 262144, 827240261886336764177, 775103122, 1978419655660313589123979, 95367433737777, 558545874543637210

Offset: 1

Author

Jason Earls, May 25 2003

Keywords

• nonn
• easy

Comments

n*log_10(2) + log_10(log_2(n)) <= length(a(n)) <= n*log_10(n). - Martin Renner, Jan 18 2012

If m = p^k is a power of a prime then a(n) = sum(p^m,i=1..k) = k*p^m is composite. - Martin Renner, Jan 31 2013

Examples

			a(6) = a(2*3) = 2^6 + 3^6 = 793.
a(8) = a(2*2*2) = 2^8 + 2^8 + 2^8 = 768.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A082813, A082814, A051674.

Programs

Maple

A082872 := proc(n)
    local ps;
    if n= 1 then
        1;
    else
        ps := ifactors(n)[2] ;
        add( op(2,p)*op(1,p)^n,p=ps) ;
    end if;
end proc: # R. J. Mathar, Mar 12 2014

Mathematica

Table[f = FactorInteger[n]; Total[Flatten[Table[Table[f[[i, 1]], {f[[i, 2]]}], {i, Length[f]}]]^n], {n, 25}] (* T. D. Noe, Feb 01 2013 *)
Table[Total[Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[n]]^n],{n,30}] (* Harvey P. Dale, Jun 10 2016 *)