A323130 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).

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

Offset: 1

Author

Rémy Sigrist, Jan 05 2019

Keywords

• nonn

Comments

This sequence is a recursive variant of A028233.

All terms belong to A164336.

Examples

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

Crossrefs

See A323129 for the variant involving the greatest prime factor.

Cf. A020639, A028233, A067029, A164336.

Programs

Mathematica

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

PARI

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

Formula

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

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