A323129 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).

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

Offset: 1

Author

Rémy Sigrist, Jan 05 2019

Keywords

• nonn
• nice
• look

Comments

This sequence is a recursive variant of A053585.

All terms belong to A164336.

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

See A323130 for the variant involving the least prime factor.

Cf. A006530, A053585, A071178, A164336.

Programs

Maple

f:= proc(n) option remember;
  local F,t;
  F:= ifactors(n)[2];
  t:= F[max[index](map(t -> t[1],F))];
  t[1]^procname(t[2]);
end proc:
f(1):= 1:
map(f, [$1..100]); # Robert Israel, Jan 07 2019

Mathematica

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

PARI

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

Formula

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

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