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A252462 Shift one instance of the largest prime one step towards smaller primes: a(1) = 1, a(2^n) = 2^(n-1), and for other numbers: a(n) = (n / prime(g)) * prime(g-1), where g = A061395(n), index of the greatest prime dividing n.

%I A252462 #21 Dec 23 2014 14:55:08
%S A252462 1,1,2,2,3,4,5,4,6,6,7,8,11,10,9,8,13,12,17,12,15,14,19,16,15,22,18,
%T A252462 20,23,18,29,16,21,26,25,24,31,34,33,24,37,30,41,28,27,38,43,32,35,30,
%U A252462 39,44,47,36,35,40,51,46,53,36,59,58,45,32,55,42,61,52,57,50,67,48,71,62,45,68,49,66,73,48,54,74,79,60
%N A252462 Shift one instance of the largest prime one step towards smaller primes: a(1) = 1, a(2^n) = 2^(n-1), and for other numbers: a(n) = (n / prime(g)) * prime(g-1), where g = A061395(n), index of the greatest prime dividing n.
%C A252462 Iterating from any n as a(n), a(a(n)), a(a(a(n))), etc. reaches 1 after A056239(n) iterations.
%H A252462 Antti Karttunen, <a href="/A252462/b252462.txt">Table of n, a(n) for n = 1..10000</a>
%F A252462 a(1) = 1; for n>1: a(n) = A008578(A061395(n)) * A052126(n). [Compare to the similar formula given for A064989.]
%F A252462 a(n) = A008578(1 + A252735(n)) * A052126(n).
%F A252462 Other identities. For all n >= 1:
%F A252462 a(2^n) = 2^(n-1).
%F A252462 For n >= 2, A001222(a(n)) = A001222(n) - A209229(n). [Number of prime divisors decreases only when n is a power of 2 larger than 1.]
%t A252462 a252462[n_Integer] := Block[{a008578, a052126, a061395, a},
%t A252462   a008578[x_] := If[x == 1, 1, Prime[x - 1]];
%t A252462   a052126[x_] := If[x == 1, 1, x/FactorInteger[x][[-1]][[1]]];
%t A252462   a061395[x_] := PrimePi[FactorInteger[x][[-1]][[1]]];
%t A252462   a[1] = 1;
%t A252462   a[x_] := a008578[a061395[x]]*a052126[x];
%t A252462 Array[a, n]]; a252462[84] (* _Michael De Vlieger_, Dec 21 2014 *)
%o A252462 (Scheme) (define (A252462 n) (if (= 1 n) n  (* (A008578 (A061395 n)) (A052126 n))))
%Y A252462 Variant: A252461.
%Y A252462 Cf. A001222, A008578, A052126, A061395, A056239, A064989, A209229, A252735.
%K A252462 nonn
%O A252462 1,3
%A A252462 _Antti Karttunen_, Dec 20 2014