A140635 Smallest positive integer having the same number of divisors as n.

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

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

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. A000005, A005179, A007416, A139770.

Cf. A019505, A138113, A061300 (sequences that can be defined in terms of this sequence).

Sequence in context: A319410 A337174 A139770 * A283465 A283466 A270492

Adjacent sequences: A140632 A140633 A140634 * A140636 A140637 A140638

Keyword

nonn

Author

Max Alekseyev, May 19 2008

Status

approved