A141568 - OEIS

%I #5 Mar 30 2012 18:52:27

%S 1,4,6,256,9,24,12,4096,1296,36,18,1536,21,48,54,65536,26,5184,28,

%T 2304,72,72,34,24576,6561,84,46656,3072,42,216,45,262144,108,104,108,

%U 331776,52,112,126,36864,57,288,60,4608,11664,136,65,393216,20736,26244,156

%N Bases and exponents in the prime decomposition of n replaced by nonprimes with these indices.

%C Start from the prime decomposition of n, not writing down exponents which equal 1; that is the list 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3,.. Replace each number i in this representation by the nonprime r(i)=A018252(i). This generates the sequence of a(n), namely r(1), r(2), r(3), r(2)^r(2), r(5), r(2)*r(3), r(7), r(2)^r(3), r(3)^r(2), r(2)*r(5), r(11), r(2)^r(2)*r(3),...

%p A018252 := proc(n) option remember ; local a; if n = 1 then 1 ; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a) ; fi; od: fi; end: A := proc(n) local a,p,e,q,ifs ; ifs := ifactors(n)[2] ; if n = 1 then RETURN(1) fi; a := 1; for p in ifs do q := A018252(op(1,p)) ; if op(2,p) > 1 then e := A018252(op(2,p)) ; else e := 1 ; fi; a := a*q^e ; od: RETURN(a) ; end: for n from 1 to 120 do printf("%d,",A(n)) ; od: # _R. J. Mathar_, Aug 21 2008

%Y Cf. A000040, A002808, A018252.

%K nonn,mult

%O 1,2

%A _Juri-Stepan Gerasimov_, Aug 17 2008

%E Edited and corrected by _R. J. Mathar_, Aug 21 2008