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%I #3 Mar 30 2012 18:52:27
%S 1,9,32,8,49,4,27,32,121,8,169,343,25,4,131072,8,1162261467,4,125,49,
%T 895430243255237372246531,4,8,3125,8192,27,9,128,841,243,961,4,4,
%U 177147,131072,78125,4,27,1369,6859,169,4,45474735088646411895751953125,8
%N Prime powers of pairs of the infinite list generated by the flat list of the factorizations of all integers.
%C Factorize n to its full extent into the list 1, 2, 3, 2*2, 5, 2*3, 7, 2*2*2, 3*3, 2*5, 11, 2*2*3,..
%C Remove delimiting commas and the multiplication signs and build new powers by pairing consecutive pairs of numbers of this list, 1^2, 3^2, 2^5, 2^3, 7^2, 2^2, 3^3, 2^5, 11^2, 2^3.. to construct the sequence.
%p pflat := proc(nmax) local a,ifs,n,p,c ; a := [1] ; for n from 2 to nmax do ifs := ifactors(n)[2] ; for p in ifs do q := op(1,p) ; for c from 1 to op(2,p) do a := [op(a),q] ; od: od: od: a ; end: pL := pflat(90) : for n from 1 to nops(pL)-2 by 2 do printf("%d,", op(n,pL)^op(n+1,pL)) ; od: # _R. J. Mathar_, Aug 21 2008
%Y Cf. A000040, A025475.
%K nonn,less
%O 1,2
%A _Juri-Stepan Gerasimov_, Aug 17 2008
%E Edited, corrected and extended by _R. J. Mathar_, Aug 21 2008