A366649 - OEIS

%I #27 Nov 19 2023 15:56:16

%S 1,1,1,2,1,3,1,4,3,5,1,4,1,7,5,8,1,9,1,5,7,11,1,8,5,13,9,7,1,5,1,16,

%T 11,17,7,9,1,19,13,8,1,7,1,11,9,23,1,16,7,25,17,13,1,27,11,8,19,29,1,

%U 5,1,31,9,32,13,11,1,17,23,7,1,9,1,37,25,19,11,13,1,16,27,41,1,7,17

%N Largest prime power (including 1) proper divisor of n, for n >= 2; a(1) = 1.

%H Robert Israel, <a href="/A366649/b366649.txt">Table of n, a(n) for n = 1..10000</a>

%p f:= proc(n) local F,t;

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

%p   if nops(F) = 1 then n/F[1,1]

%p   else max(map(t -> t[1]^t[2], F))

%p   fi

%p end proc:

%p f(1):= 1:

%p map(f, [$1..100]); # _Robert Israel_, Nov 19 2023

%t Join[{1}, Table[Last[Select[Divisors[n], # < n && (# == 1 || PrimePowerQ[#]) &]], {n, 2, 85}]]

%t a[n_] := Module[{f = FactorInteger[n]}, If[Length[f] == 1, f[[1, 1]]^(f[[1, 2]] - 1), Max[Power @@@ f]]]; Array[a, 100] (* _Amiram Eldar_, Oct 19 2023 *)

%o (PARI) a(n) = if (n==1, 1, my(d=divisors(n)); vecmax(select(x->(isprimepower(x) || (x==1)), Vec(d, #d-1)))); \\ _Michel Marcus_, Oct 17 2023

%Y Cf. A032742, A034699, A063928, A085392, A089384, A093803.

%K nonn,look

%O 1,4

%A _Ilya Gutkovskiy_, Oct 17 2023