

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
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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).


LINKS



FORMULA



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]]


PROG

(PARI) a(n) = {nd = numdiv(n); for (i=1, n1, 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


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



