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A224787 Sum of cubes of prime factors of n (counted with multiplicity).

%I A224787 #17 Mar 25 2025 10:47:06
%S A224787 0,8,27,16,125,35,343,24,54,133,1331,43,2197,351,152,32,4913,62,6859,
%T A224787 141,370,1339,12167,51,250,2205,81,359,24389,160,29791,40,1358,4921,
%U A224787 468,70,50653,6867,2224,149,68921,378,79507,1347,179,12175,103823,59,686,258
%N A224787 Sum of cubes of prime factors of n (counted with multiplicity).
%H A224787 T. D. Noe, <a href="/A224787/b224787.txt">Table of n, a(n) for n = 1..10000</a>
%p A224787 A224787 := proc(n)
%p A224787     local a,pe,p,e ;
%p A224787     a := 0 ;
%p A224787     for pe in ifactors(n)[2] do
%p A224787         p := op(1,pe) ;
%p A224787         e := op(2,pe) ;
%p A224787         a := a+e*p^3;
%p A224787     end do:
%p A224787     a ;
%p A224787 end proc:
%p A224787 seq(A224787(n),n=1..20) ; # _R. J. Mathar_, Mar 25 2025
%t A224787 Join[{0}, Table[{p, e} = Transpose[FactorInteger[n]]; Total[e*p^3], {n, 2, 50}]] (* _T. D. Noe_, Apr 17 2013 *)
%Y A224787 Cf. A001414, A067666.
%K A224787 nonn
%O A224787 1,2
%A A224787 _Jiwon Lee_, Apr 17 2013
%E A224787 Extended by _T. D. Noe_, Apr 17 2013