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A139770 Smallest number having at least as many divisors as n. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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
LINKS
FORMULA
a(n) = A061799(A000005(n)).
EXAMPLE
16 has 5 divisors; smallest number with at least 5 divisors is 12 with 6 divisors, thus a(16) = 12.
MATHEMATICA
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 *)
PROG
(PARI) a(n) = {nd = numdiv(n); for (i=1, n-1, if (numdiv(i) >= nd, return (i)); ); return (n); } \\ Michel Marcus, Jun 14 2013
(Python)
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
CROSSREFS
Sequence in context: A122457 A319410 A337174 * A140635 A283465 A283466
KEYWORD
nonn
AUTHOR
J. Lowell, May 20 2008
EXTENSIONS
Edited and extended by Ray Chandler, May 24 2008
STATUS
approved

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Last modified February 24 02:58 EST 2024. Contains 370288 sequences. (Running on oeis4.)