A061300 -id:A061300 - cp's OEIS frontend

A357582 a(n) = A061300(n+1)/A061300(n).

1, 2, 6, 30, 154, 1105, 4788, 20677, 216931, 858925, 7105392, 5546059, 2018025900, 1480452337, 3238556831, 107972737, 18425956230000, 4683032671, 14053747110612300, 160436746661, 33809725025123, 15260431896321667, 1583855315457687090000

Offset: 0

J. Lowell, Oct 04 2022

It is not known if the ratios A061300(n+1)/A061300(n) are always integer, but so far (for the listed terms) they are. - Max Alekseyev, Sep 05 2023

			a(5) = 1105 as A061300(5+1) / A061300(5) = 61261200 / 55440 = 1105.

Max Alekseyev, Table of n, a(n) for n = 0..29

Cf. A061300.

A061300[n_Integer?NonNegative] := A061300[n] = Module[{fact = n!, num = 1}, Monitor[While[Length@Divisors@num != fact, num++]; num, {n, num}]]; a[n_] := A061300[n + 1]/A061300[n]; Table[a[n], {n, 0, 4}] (* Robert P. P. McKone, Sep 07 2023 *)

a(11)-a(21) from David A. Corneth, Oct 05 2022

a(22)-a(29) from Max Alekseyev, Sep 05 2023

A061307 Duplicate of A061300.

Original entry on oeis.org

1, 1, 2, 12, 360, 55440, 61261200, 293318625600, 6064949221531200

Offset: 0

dead

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

Original entry on oeis.org

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

Max Alekseyev, May 19 2008

nonn

a(n) <= n for all n. Moreover, a(n) = n if and only if n belongs to A005179 or A007416.

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

Cf. A000005, A005179, A007416, A139770.

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

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 *)

A140635(n) = { my(nd = numdiv(n)); for (i=1, n, if (numdiv(i) == nd, return (i))); }; \\ After A139770, Antti Karttunen, May 27 2017

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) = A005179(A000005(n)).

cp's OEIS Frontend

A357582 a(n) = A061300(n+1)/A061300(n).

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A061307 Duplicate of A061300.

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

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