A323129 - OEIS

%I #19 Mar 01 2023 01:50:18

%S 1,2,3,4,5,3,7,8,9,5,11,3,13,7,5,16,17,9,19,5,7,11,23,3,25,13,27,7,29,

%T 5,31,32,11,17,7,9,37,19,13,5,41,7,43,11,5,23,47,3,49,25,17,13,53,27,

%U 11,7,19,29,59,5,61,31,7,8,13,11,67,17,23,7,71,9,73

%N a(1) = 1, and for any n > 1, let p be the greatest prime factor of n, and e be its exponent, then a(n) = p^a(e).

%C This sequence is a recursive variant of A053585.

%C All terms belong to A164336.

%H Robert Israel, <a href="/A323129/b323129.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) <= n with equality iff n belongs to A164336.

%F a(n) = A006530(n)^a(A071178(n)) for any n > 1.

%e a(1458) = a(2 * 3^6) = 3^a(6) = 3^a(2*3) = 3^3 = 27.

%p f:= proc(n) option remember;

%p   local F,t;

%p   F:= ifactors(n)[2];

%p   t:= F[max[index](map(t -> t[1],F))];

%p   t[1]^procname(t[2]);

%p end proc:

%p f(1):= 1:

%p map(f, [$1..100]); # _Robert Israel_, Jan 07 2019

%t Nest[Append[#, Last@ FactorInteger[Length[#] + 1] /. {p_, e_} :> p^#[[e]] ] &, {1}, 72] (* _Michael De Vlieger_, Jan 07 2019 *)

%o (PARI) a(n) = if (n==1, 1, my (f=factor(n)); f[#f~,1]^a(f[#f~,2]))

%Y See A323130 for the variant involving the least prime factor.

%Y Cf. A006530, A053585, A071178, A164336.

%K nonn,nice,look

%O 1,2

%A _Rémy Sigrist_, Jan 05 2019