A284476 Smallest number with same factorization shape as n.

1, 2, 2, 4, 2, 6, 2, 4, 4, 6, 2, 12, 2, 6, 6, 16, 2, 12, 2, 12, 6, 6, 2, 12, 4, 6, 4, 12, 2, 30, 2, 4, 6, 6, 6, 36, 2, 6, 6, 12, 2, 30, 2, 12, 12, 6, 2, 48, 4, 12, 6, 12, 2, 12, 6, 12, 6, 6, 2, 60, 2, 6, 12, 64, 6, 30, 2, 12, 6, 30, 2, 36, 2, 6, 12, 12, 6, 30

Offset: 1

Author

Rémy Sigrist, Mar 27 2017

Keywords

• nonn

Comments

A284456 defines the factorization shape of a number.

A284456 corresponds to the fixed points of this sequence.

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A284456.

Programs

PARI

a(n) = my (f=factor(n)); \
       my (x=vecsort(vector(#f~, i, a(f[i,2])),,4)); \
       return (prod(i=1, #x, prime(i)^x[i]))

Formula

To compute a(n):

1) Factorize n: n = p_1^e_1 * ... * p_k^e_k,

2) Compute a(e_i) for i=1..k,

3) Sort the values computed at step 2 in descending order (keeping duplicates): you obtain, say, f_1 >= ... >= f_k,

4) a(n) = Prod_{i=1..k} prime(i)^f_i.