A300518 The greatest prime factor of the squarefree part of n, or 1 if n is square.

1, 2, 3, 1, 5, 3, 7, 2, 1, 5, 11, 3, 13, 7, 5, 1, 17, 2, 19, 5, 7, 11, 23, 3, 1, 13, 3, 7, 29, 5, 31, 2, 11, 17, 7, 1, 37, 19, 13, 5, 41, 7, 43, 11, 5, 23, 47, 3, 1, 2, 17, 13, 53, 3, 11, 7, 19, 29, 59, 5, 61, 31, 7, 1, 13, 11, 67, 17, 23, 7, 71, 2, 73, 37

Offset: 1

Author

Peter Kagey, Mar 07 2018

Keywords

• nonn
• easy

Comments

The greatest prime factor of n that has an odd exponent in the prime factorization of n, or 1 is no such prime exists. - Amiram Eldar, Oct 28 2024

Examples

			For n = 15000 = 5^4 * 3 * 2^3, 3 is the greatest unpaired prime, so a(15000) = 3.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000
• Hugo Pfoertner, Illustration of first 10^5 terms, zoom into central part to see nice patterns.

Crossrefs

Cf. A006530, A007913.

Programs

Magma

[#f eq 0 select 1 else f[#f][1] where f is Factorization(Squarefree(n)): n in [1..90]]; // Vincenzo Librandi, Mar 08 2018

Maple

a:= n-> max(1, seq(i[1]^irem(i[2], 2), i=ifactors(n)[2])):
seq(a(n), n=1..100);  # Alois P. Heinz, Mar 07 2018

Mathematica

Array[FactorInteger[Sqrt[#] /. (c_: 1)*a_^(b_: 0) :> (c*a^b)^2][[-1, 1]] &, 74] (* Michael De Vlieger, Mar 10 2018, after Bill Gosper at A007913 *)

PARI

gpf(n) = if (n==1, 1, vecmax(factor(n)[,1]));
a(n) = gpf(core(n)); \\ Michel Marcus, Mar 08 2018

PARI

a(n) = {my(f = factor(n)); forstep(i = #f~, 1, -1, if(f[i,2] % 2, return(f[i, 1]))); 1;} \\ Amiram Eldar, Oct 28 2024

Formula

a(n) = A006530(A007913(n)).