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A164336
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a(1)=1. Thereafter, all terms are primes raised to the values of earlier terms of the sequence.
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28
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1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227
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OFFSET
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1,2
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COMMENTS
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These are the values of exponent towers consisting completely of primes coefficients. (For example, p^(q^(r^(s^..))), all variables being primes.) This sequence first differs from the terms of A096165, after the initial 1 in this sequence, when 18446744073709551616 = 2^64 occurs in A096165 but not in this sequence.
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LINKS
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MAPLE
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q:= n-> is(n=1 or (l-> nops(l)=1 and q(l[1, 2]))(ifactors(n)[2])):
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MATHEMATICA
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Block[{a = {1}}, Do[If[Length@ # == 1 && MemberQ[a, First@ #], AppendTo[a, i]] &[FactorInteger[i][[All, -1]]], {i, 2, 227}]; a] (* Michael De Vlieger, Aug 31 2017 *)
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PROG
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(PARI) L=1000; S=[1]; SS=[]; while(#S!=#SS, SS=S; S=[]; for(i=1, #SS, forprime(p=2, floor(L^(1/SS[i])), S=concat(S, p^SS[i]))); S=eval(setunion(S, SS))); vecsort(S) \\ Hagen von Eitzen, Oct 03 2009
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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