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A245447 Permutation of natural numbers: a(n) = A048673(A048673(n)).

%I A245447 #15 May 16 2017 08:50:52
%S A245447 1,2,3,4,5,14,8,17,9,7,6,15,13,10,38,22,11,35,23,122,50,32,18,86,25,
%T A245447 26,138,74,41,30,12,101,33,16,43,64,28,39,24,81,20,45,68,31,176,59,63,
%U A245447 171,34,62,203,72,53,239,44,76,47,27,19,125,29,149,218,277,158,182,113,71,40
%N A245447 Permutation of natural numbers: a(n) = A048673(A048673(n)).
%H A245447 Antti Karttunen, <a href="/A245447/b245447.txt">Table of n, a(n) for n = 1..10001</a>
%H A245447 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A245447 a(n) = A048673(A048673(n)).
%F A245447 a(n) = (1/2) * (1 + A003961((1/2) * (1+A003961(n)))). [Where A003961(n) shifts the prime factorization of n one step left.]
%F A245447 a(n) = ((A003961(A243501(n)/2)) + 1) / 2  = ((A003961(A243501(n))/3) + 1) / 2.
%F A245447 For all n >= 1, A243501(n) = A243502(a(n)).
%t A245447 b[p_?PrimeQ] := b[p] = Prime[PrimePi[p] + 1]; b[1] = 1; b[n_] := b[n] = Times @@ (b[First[#]]^Last[#]&) /@ FactorInteger[n];
%t A245447 A048673[n_] := (b[n] + 1)/2;
%t A245447 a[n_] := A048673[A048673[n]];
%t A245447 Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, May 16 2017 *)
%o A245447 (Scheme) (define (A245447 n) (A048673 (A048673 n)))
%Y A245447 Inverse: A245448.
%Y A245447 Fixed points: A245449.
%Y A245447 Cf. A048673, A243501, A243502.
%K A245447 nonn
%O A245447 1,2
%A A245447 _Antti Karttunen_, Jul 22 2014