A009287 -id:A009287 - cp's OEIS frontend

A036460 Erroneous version of A009287 (the 2 should be omitted).

2, 3, 4, 6, 12, 60, 5040, 293318625600

Offset: 0

dead

Let b(n) = min k: d^k(n) = 2, where d(n) is the number of divisors of n. Then the given values correctly identify records of b(n). But see A251483 for a slight variant with more values.

A061080 Another erroneous version of A009287.

Original entry on oeis.org

3, 4, 6, 12, 72, 559872

Offset: 1

dead

A182857 Smallest number that requires exactly n iterations to reach a fixed point under the x -> A181819(x) map.

Original entry on oeis.org

1, 3, 4, 6, 12, 60, 2520, 1286485200, 35933692027611398678865941374040400000

Offset: 0

Matthew Vandermast, Jan 05 2011

nonn

a(9) has 296 digits.
Related to Levine's sequence (A011784): A011784(n) = A001222(a(n)) = A001221(a(n+1)) = A051903(a(n+2)) = A071625(a(n+2)). Also see A182858.
Values of n where A182850(n) increases to a record.
The multiplicity of prime(k) in a(n+1) is the k-th largest prime index of a(n), which is A296150(a(n),k). - Gus Wiseman, May 13 2018

			From _Gus Wiseman_, May 13 2018: (Start)
Like A001462 the following sequence of multisets whose Heinz numbers belong to this sequence is a run-length describing sequence, as the number of k's in row n + 1 is equal to the k-th term of row n.
{2}
{1,1}
{1,2}
{1,1,2}
{1,1,2,3}
{1,1,1,2,2,3,4}
{1,1,1,1,2,2,2,3,3,4,4,5,6,7}
{1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,7,7,7,8,8,9,9,10,10,11,12,13,14}
(End)

Gus Wiseman, Table of n, a(n) for n = 0..9

Cf. A001462, A007755, A007916, A009287, A012257, A112798, A181819, A182850-A182858, A296150, A304455, A304464, A304465.

Prepend[Function[m,Times@@Prime/@m]/@NestList[Join@@Table[Table[i,{Reverse[#][[i]]}],{i,Length[#]}]&,{2},8],1] (* Gus Wiseman, May 13 2018 *)

For n > 0, a(n) = A181819(a(n+1)). For n > 1, a(n) = A181821(a(n-1)).

A061300 Least number whose number of divisors is n!.

Original entry on oeis.org

1, 1, 2, 12, 360, 55440, 61261200, 293318625600, 6064949221531200, 1315675499575984747200, 1130066578473302698988760000, 8029566026151577210973143393920000, 44532446925432190155112500678140561280000, 89867631285897528426742043782255216503577152000000

Offset: 0

Amarnath Murthy and Labos Elemer, Apr 26 2001

a(n) = A037019(n!) for all n <= 12 except for 4. I conjecture that this remains true for all larger n, i.e., 4! is the only "exceptional" factorial (see A037019). - David Wasserman, Jun 13 2002
Conjecture is confirmed for n <= 30. - Max Alekseyev, Sep 05 2023
Alternate definition: a(0)=1; for n >= 1, smallest number with same number of divisors as A006939(n-1). - J. Lowell, May 20 2008

			a(3) = 12 and tau(12) = 6 = 3!.

Max Alekseyev, Table of n, a(n) for n = 0..30

Cf. A000005, A005179, A007304, A006939, A037019, A000142, A072066, A009287.

Cf. A140635.

a(n) = A005179(n!); for example, A005179(120)=55440.

a(n) = Min{x| A000005(x)=n!}; for example, A000005(55440)=120 and 55440 is minimal.

More terms from David Wasserman, Jun 13 2002

Terms a(12) onward from Max Alekseyev, Sep 05 2023

A251483 Position of first occurrence of n in A036459.

Original entry on oeis.org

1, 3, 4, 6, 12, 60, 5040, 293318625600, 635197862493622653217009501211465321419691071212633792891415680000000000

Offset: 0

Ivan Neretin, Mar 29 2015

nonn

			For n=7, a(7) = 293318625600 -> 5040 -> 60 -> 12 -> 6 -> 4 -> 3 -> 2.
For n=8, a(8) -> 1111523212800 -> 5040 -> 60 -> 12 -> 6 -> 4 -> 3 -> 2.

Coincides with A009287 for n <= 7 (only).

a036459(n) = {if (n<=2, return(0)); nb = 1; while ((nd = numdiv(n)) > 2, n = nd; nb++); nb;}
a(n) = {k = 1; while (a036459(k) != n, k++); k;} \\ Michel Marcus, Oct 28 2015

A037025 a(1) = 8; a(n) = least k with d(k) = a(n-1), where d(k) is the number of divisors of k.

Original entry on oeis.org

8, 24, 360, 3603600, 2549066103582535692163008000000

Offset: 1

Donald S. McDonald

Unless a(5) is an "exceptional" (or "extraordinary") number (see A072066), a(6) = 2^30 * 3^28 * 5^22 * 7^18 * 11^16 * 13^16 * 17^12 * 19^12 * 23^10 * 29^10 * 31^10 * 37^10 * 41^6 * 43^6 * 47^6 * 53^6 * 59^4 * 61^4 * 67^4 * 71^4 * 73^4 * 79^4 * 83^2 * 89^2 * 97^2 * 101^2 * 103^2 * 107^2 * 109^2 * 113^2 * 127^2 * 131^2 * 137 * 139 * 149 * 151 * 157 * 163 * 167 * 173 * 179 * 181 * 191 * 193 = 1.77955...*10^327 (a 328-digit number). - Jon E. Schoenfield, Sep 07 2023

Cf. A000005, A009287.

lista(nn) = {a=8; print1(a, ", "); for (n=2, nn, k=1; while(numdiv(k) != a, k++); print1(k, ", "); a = k;);} \\ Michel Marcus, Feb 17 2015

One more term from Naohiro Nomoto, Jun 28 2001

A133454 Chain of 6 highly composite numbers generated when subject to the recurrence relation tau(a(n+1)) = a(n), with a(0)=3, where tau(n) is the number-of-divisors function A000005(n).

Original entry on oeis.org

4, 6, 12, 60, 5040, 293318625600

Offset: 1

Lekraj Beedassy, Dec 22 2007

We omit the seed a(0) from the sequence and keep the offset at 1, because 3 is not highly composite. - R. J. Mathar, Jun 20 2021

			Since 4 is the HCN with 3 divisors, we have tau(4) = 3 and therefore a(1)=4; the HCN with 4 divisors is 6, so that tau(6) = 4 and hence a(2)=6; the HCN with 6 divisors is 12 so that tau(12) = 6, implying a(3)=12, ...

Cf. A002182.

A finite subsequence of A009287.

cp's OEIS Frontend

A036460 Erroneous version of A009287 (the 2 should be omitted).

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A061080 Another erroneous version of A009287.

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A182857 Smallest number that requires exactly n iterations to reach a fixed point under the x -> A181819(x) map.

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A061300 Least number whose number of divisors is n!.

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A251483 Position of first occurrence of n in A036459.

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A037025 a(1) = 8; a(n) = least k with d(k) = a(n-1), where d(k) is the number of divisors of k.

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A133454 Chain of 6 highly composite numbers generated when subject to the recurrence relation tau(a(n+1)) = a(n), with a(0)=3, where tau(n) is the number-of-divisors function A000005(n).

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