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A140635
Smallest positive integer having the same number of divisors as n.
13
1, 2, 2, 4, 2, 6, 2, 6, 4, 6, 2, 12, 2, 6, 6, 16, 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, 64, 6, 24, 2, 12, 6, 24, 2, 60, 2, 6, 12, 12, 6, 24, 2, 48, 16, 6, 2, 60, 6, 6, 6, 24, 2
OFFSET
1,2
COMMENTS
a(n) <= n for all n. Moreover, a(n) = n if and only if n belongs to A005179 or A007416.
LINKS
FORMULA
a(n) = A005179(A000005(n)).
MATHEMATICA
a140635[n_] := NestWhile[#+1&, 1, DivisorSigma[0, n]!=DivisorSigma[0, #]&]
a140635[{m_, n_}] := Map[a140635, Range[m, n]]
a140635[{1, 89}] (* Hartmut F. W. Hoft, Jun 13 2023 *)
PROG
(PARI) A140635(n) = { my(nd = numdiv(n)); for (i=1, n, if (numdiv(i) == nd, return (i))); }; \\ After A139770, Antti Karttunen, May 27 2017
(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
Cf. A019505, A138113, A061300 (sequences that can be defined in terms of this sequence).
Sequence in context: A319410 A337174 A139770 * A283465 A283466 A270492
KEYWORD
nonn
AUTHOR
Max Alekseyev, May 19 2008
STATUS
approved