A381613 If n = Product (p_j^k_j) then a(n) = Product (min(p_j, k_j)), with a(1) = 1.

1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 2, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1

Offset

1,4

Comments

First differs from A323308 at n = 27.

Links

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

Formula

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + (1/p - 1/p^p)/(p-1)) = 1.59383299054679951264... . - Amiram Eldar, Mar 07 2025

Example

a(18) = 2 because 18 = 2^1*3^2, min(2,1) = 1, min(3,2) = 2 and 1*2 = 2.
a(300) = 4 because 300 = 2^2*3^1*5^2, min(2,2) = 2, min(3,1) = 1, min(5,2) = 2 and 2*1*2 = 4.

Mathematica

A381613[n_] := Times @@ Min @@@ FactorInteger[n];
Array[A381613, 100]

Prog

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

Crossrefs

Cf. A008473, A008477, A035306, A323308, A369008, A381588, A381614.

Sequence in context: A307848 A358260 A368978 * A381403 A255326 A085424

Adjacent sequences: A381610 A381611 A381612 * A381614 A381615 A381616

Keyword

nonn,mult,easy

Author

Paolo Xausa, Mar 01 2025

Status

approved