Search: id:A067688
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%I A067688
%S A067688 4,16,27,256,3125,19683,65536,823543,1096744,2836295,4294967296,
%T A067688 4473671462
%N A067688 Composite n such that for some integer r, n equals the sum of the r-th 
               powers of the prime factors of n (counted with multiplicity).
%C A067688 Every prime is the sum of the first powers of its prime factors, so only 
               composite numbers have been considered in this sequence.
%C A067688 Every integer of the form p^p^k with p prime and k>0 is in the sequence, 
               since it equals the sum of the (p^k - k)-th powers of its prime factors. 
               The first 8 terms of the sequence are of this form, but 1096744 = 
               2^3*11^3*103 and 2836295 = 5*7*11*53*139 are not.
%C A067688 4473671462=2*13*179*593*1621 is also not a prime power.
%e A067688 The sum of the cubes of the prime factors of 1096744 is 3*2^3 + 3*11^3 
               + 103^3 = 1096744.
%t A067688 For[n=2, True, n++, If[ !PrimeQ[n], For[r=1; fn=FactorInteger[n]; s=0, 
               s<=n, r++, s=Plus@@((#[[2]]#[[1]]^r)&/@fn); If[s==n, Print[{n, r}]]]]]
%Y A067688 Cf. A068916, A081177 (for values of r).
%Y A067688 Sequence in context: A072653 A008478 A111260 this_sequence A046358 A046366 
               A097374
%Y A067688 Adjacent sequences: A067685 A067686 A067687 this_sequence A067689 A067690 
               A067691
%K A067688 nonn
%O A067688 1,1
%A A067688 Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Feb 04 2002
%E A067688 Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Mar 07 2002
%E A067688 More terms from Jud McCranie (j.mccranie(AT)comcast.net), Mar 10 2003

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