A304180 If n = Product (p_j^k_j) then a(n) = max{p_j}^max{k_j}.

1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 9, 13, 7, 5, 16, 17, 9, 19, 25, 7, 11, 23, 27, 25, 13, 27, 49, 29, 5, 31, 32, 11, 17, 7, 9, 37, 19, 13, 125, 41, 7, 43, 121, 25, 23, 47, 81, 49, 25, 17, 169, 53, 27, 11, 343, 19, 29, 59, 25, 61, 31, 49, 64, 13, 11, 67, 289, 23, 7, 71, 27, 73, 37, 25

Offset: 1

Author

Ilya Gutkovskiy, May 07 2018

Keywords

• nonn

Examples

			a(40) = 125 because 40 = 2^3*5^1, max{2,5} = 5, max{3,1} = 3 and 5^3 = 125.
		

Links

• Ilya Gutkovskiy, Scatter plot of a(n) up to n=100000.
• Eric Weisstein's World of Mathematics, Greatest Prime Factor.
• Index entries for sequences computed from exponents in factorization of n.

Crossrefs

Cf. A000040, A000961 (fixed points), A002110, A005117, A006530, A034699, A051903, A053585, A073482, A081810, A304181.

Programs

Mathematica

Table[(FactorInteger[n][[-1, 1]])^(Max @@ Last /@ FactorInteger[n]), {n, 75}]

PARI

a(n) = if(n == 1, 1, my(f = factor(n), p = f[, 1], e = f[, 2]); vecmax(p)^vecmax(e)); \\ Amiram Eldar, Sep 08 2024

Formula

a(n) = A006530(n)^A051903(n).

a(p^k) = p^k where p is a prime.

a(A005117(k)) = A073482(k).

a(A002110(k)) = A000040(k).