A323130 - OEIS

%I #11 Jan 08 2019 08:37:48

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

%T 31,32,3,2,5,4,37,2,3,8,41,2,43,4,9,2,47,16,49,2,3,4,53,2,5,8,3,2,59,

%U 4,61,2,9,4,5,2,67,4,3,2,71,8,73,2,3,4,7,2,79

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

%C This sequence is a recursive variant of A028233.

%C All terms belong to A164336.

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

%F a(n) = A020639(n)^a(A067029(n)) for any n > 1.

%e a(320) = a(2^6 * 5) = 2^a(6) = 2^a(2*3) = 2^2 = 4.

%t Nest[Append[#, First@ FactorInteger[Length[#] + 1] /. {p_, e_} :> p^#[[e]] ] &, {1}, 78] (* _Michael De Vlieger_, Jan 07 2019 *)

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

%Y See A323129 for the variant involving the greatest prime factor.

%Y Cf. A020639, A028233, A067029, A164336.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Jan 05 2019