A135874 Multiply the positive divisors of n in order (starting at 1). a(n) is the smallest such partial product that is >= n.

1, 2, 3, 8, 5, 6, 7, 8, 27, 10, 11, 24, 13, 14, 15, 64, 17, 36, 19, 40, 21, 22, 23, 24, 125, 26, 27, 56, 29, 30, 31, 64, 33, 34, 35, 144, 37, 38, 39, 40, 41, 252, 43, 88, 135, 46, 47, 144, 343, 100, 51, 104, 53, 324, 55, 56, 57, 58, 59, 120

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

The positive divisors of 12 are 1,2,3,4,6,12. Checking the partial products: 1=1, 1*2=2, 1*2*3=6, 1*2*3*4=24, 1*2*3*4*6 = 144, 1*2*3*4*6*12 = 1728. 24 is the smallest such product which is >= 12. So a(12) = 24.

Maple

with(numtheory): a:=proc(n) local div, j, pr: div:=divisors(n): for j while product(div[i], i=1..j)< n do pr:=product(div[i], i=1..j+1) end do: pr end proc: 1, seq(a(n), n=2..60); # Emeric Deutsch, Dec 18 2007

Mathematica

Table[SelectFirst[FoldList[Times, Divisors[n]], #>=n&], {n, 60}] (* The program uses the SelectFirst function from Mathematica version 10 *) (* Harvey P. Dale, Sep 06 2015 *)

Crossrefs

Cf. A135875.

Sequence in context: A268385 A093928 A356191 * A372329 A138682 A065632

Adjacent sequences: A135871 A135872 A135873 * A135875 A135876 A135877

Keyword

nonn

Author

Leroy Quet, Dec 03 2007

Extensions

More terms from Emeric Deutsch, Dec 18 2007

Status

approved