A304233 If n = Product (p_j^k_j) then a(n) = min{p_j^k_j}*max{p_j^k_j}.

1, 4, 9, 16, 25, 6, 49, 64, 81, 10, 121, 12, 169, 14, 15, 256, 289, 18, 361, 20, 21, 22, 529, 24, 625, 26, 729, 28, 841, 10, 961, 1024, 33, 34, 35, 36, 1369, 38, 39, 40, 1681, 14, 1849, 44, 45, 46, 2209, 48, 2401, 50, 51, 52, 2809, 54, 55, 56, 57, 58, 3481, 15, 3721, 62, 63, 4096, 65

Offset: 1

Author

Ilya Gutkovskiy, May 08 2018

Keywords

• nonn

Examples

			a(60) = 15 because 60 = 2^2*3*5, min{2^2,3,5} = 3, max{2^2,3,5} = 5 and 3*5 = 15.
		

Links

• Ilya Gutkovskiy, Logarithmic scatter plot of a(n) up to n=30000
• Eric Weisstein's World of Mathematics, Prime Factorization

Crossrefs

Cf. A000977 (numbers n such that a(n) < n), A002110, A007774 (fixed points), A034684, A034699, A066048, A100484, A141809.

Programs

Mathematica

a[n_] := Min[#[[1]]^#[[2]] & /@FactorInteger[n]] Max[#[[1]]^#[[2]] & /@FactorInteger[n]]; Table[a[n], {n, 65}]

Formula

a(n) = A034684(n)*A034699(n).

a(p^k) = p^(2*k) where p is a prime.

a(A002110(k)) = A100484(k).