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%I #12 Aug 09 2024 05:06:55
%S 1,2,3,4,5,7,8,9,11,13,17,19,23,25,27,29,31,32,37,41,43,47,49,53,59,
%T 61,67,71,73,79,83,89,97,101,103,107,109,113,121,125,127,131,137,139,
%U 149,151,157,163,167,169,173,179,181,191,193,197,199,211,223,227,229,233
%N Numbers of the form p^k, where p is a prime and k is a Fibonacci number.
%H Amiram Eldar, <a href="/A115975/b115975.txt">Table of n, a(n) for n = 1..10000</a>
%t With[{nn=60},Take[Join[{1},Union[First[#]^Last[#]&/@Union[Flatten[ Outer[List,Prime[Range[nn]],Fibonacci[Range[nn/6]]],1]]]],70]] (* _Harvey P. Dale_, Jun 05 2012 *)
%t fib[lim_] := Module[{s = {}, f = 1, k = 2}, While[f <= lim, AppendTo[s, f]; k++; f = Fibonacci[k]]; s]; seq[max_] := Module[{s = {1}, p = 2, e = 1, f = {}}, While[e > 0, e = Floor[Log[p, max]]; If[f == {}, f = fib[e], f = Select[f, # <= e &]]; s = Join[s, p^f]; p = NextPrime[p]]; Sort[s]]; seq[250] (* _Amiram Eldar_, Aug 09 2024 *)
%o (PARI) {m=240;v=Set([]);forprime(p=2,m,i=0;while((s=p^fibonacci(i))<m,v=setunion(v,Set(s));i++)); v=vecsort(eval(v));for(j=1,#v,print1(v[j],","))}
%Y Subsequence of A000961 (powers of primes).
%Y Cf. A117245 (partial sums).
%Y Subsequences: A000040, A001248, A030078, A050997, A138031, A179645.
%K easy,nonn
%O 1,2
%A _Giovanni Teofilatto_, Mar 15 2006; corrected Apr 23 2006
%E Edited and corrected by _Klaus Brockhaus_, Apr 25 2006