A381614 If n = Product (p_j^k_j) then a(n) = Product (max(p_j, k_j)), with a(1) = 1.

1, 2, 3, 2, 5, 6, 7, 3, 3, 10, 11, 6, 13, 14, 15, 4, 17, 6, 19, 10, 21, 22, 23, 9, 5, 26, 3, 14, 29, 30, 31, 5, 33, 34, 35, 6, 37, 38, 39, 15, 41, 42, 43, 22, 15, 46, 47, 12, 7, 10, 51, 26, 53, 6, 55, 21, 57, 58, 59, 30, 61, 62, 21, 6, 65, 66, 67, 34, 69, 70, 71, 9, 73

Offset: 1

Author

Paolo Xausa, Mar 01 2025

Keywords

• nonn
• mult
• easy

Examples

			a(18) = 6 because 18 = 2^1*3^2, max(2,1) = 2, max(3,2) = 3 and 2*3 = 6.
a(300) = 30 because 300 = 2^2*3^1*5^2, max(2,2) = 2, max(3,1) = 3, max(5,2) = 5 and 2*3*5 = 30.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008473, A008477, A035306, A065463, A369008, A381588, A381613.

Programs

Mathematica

A381614[n_] := Times @@ Max @@@ FactorInteger[n];
Array[A381614, 100]

PARI

a(n) = my(f=factor(n)); prod(i=1, #f~, max(f[i,1], f[i,2])); \\ Michel Marcus, Mar 02 2025

Formula

a(p) = p, for p prime.

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = A065463 * Product_{p prime} (1 + 1/((p^2-1)*(p^2+p-1)*p^(2*p-2))) = 0.71628338157754073004... . - Amiram Eldar, Mar 07 2025