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

1,2

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

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.

Prog

(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]))

Crossrefs

Cf. A284456.

Sequence in context: A054704 A143525 A086087 * A082174 A278235 A074369

Adjacent sequences: A284473 A284474 A284475 * A284477 A284478 A284479

Keyword

nonn

Author

Rémy Sigrist, Mar 27 2017

Status

approved