A365263 -id:A365263 - cp's OEIS frontend

A139770 Smallest number having at least as many divisors as n.

1, 2, 2, 4, 2, 6, 2, 6, 4, 6, 2, 12, 2, 6, 6, 12, 2, 12, 2, 12, 6, 6, 2, 24, 4, 6, 6, 12, 2, 24, 2, 12, 6, 6, 6, 36, 2, 6, 6, 24, 2, 24, 2, 12, 12, 6, 2, 48, 4, 12, 6, 12, 2, 24, 6, 24, 6, 6, 2, 60, 2, 6, 12, 24, 6, 24, 2, 12, 6, 24, 2, 60, 2, 6, 12, 12, 6, 24, 2, 48, 12, 6, 2, 60, 6, 6, 6, 24, 2

Offset: 1

J. Lowell, May 20 2008

nonn

Similar to A140635, except that a(n) is allowed to have more divisors than n.
a(n) <= n for all n. Moreover, a(n) = n if and only if n belongs to A061799 (or equivalently A002182).
When n is prime, a(n) = 2. - Michel Marcus, Jun 14 2013
For numbers k such that a(k) and A140635(k) are not equal see A365263. - Michel Marcus, Aug 31 2023

			16 has 5 divisors; smallest number with at least 5 divisors is 12 with 6 divisors, thus a(16) = 12.

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000005, A002182, A061799, A140635, A365263.

a139770[n_] := NestWhile[#+1&, 1, DivisorSigma[0, n]>DivisorSigma[0, #]&]
a139770[{m_, n_}] := Map[a139770, Range[m, n]]
a139770[{1, 89}] (* Hartmut F. W. Hoft, Jun 13 2023 *)

a(n) = {nd = numdiv(n); for (i=1, n-1, if (numdiv(i) >= nd, return (i));); return (n);} \\ Michel Marcus, Jun 14 2013

from sympy import divisor_count as d
def a(n):
    x=d(n)
    m=1
    while True:
        if d(m)>=x: return m
        else: m+=1 # Indranil Ghosh, May 27 2017

a(n) = A061799(A000005(n)).

Edited and extended by Ray Chandler, May 24 2008

cp's OEIS Frontend

A139770 Smallest number having at least as many divisors as n.

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