A133411 -id:A133411 - cp's OEIS frontend

A330744 Primorial deflation of A133411(n), where A133411(n) is the smallest highly composite number of the form k*a(n-1) where k is an integer greater than 1.

1, 2, 4, 6, 12, 24, 40, 60, 84, 168, 336, 528, 792, 936, 1872, 2448, 2736, 4560, 5520, 8280, 11592, 23184, 29232, 31248, 62496, 74592, 124320, 137760, 144480, 157920, 315840, 356160, 559680, 623040, 644160, 966240, 1061280, 1124640, 1686960, 1734480, 2049840, 2218320, 2330640, 2499120, 4165200, 4539600, 4726800, 4820400

Offset: 1

Antti Karttunen, Jan 10 2020

nonn

a(n) is the unique integer k such that A108951(k) = A133411(n).
Note that this sequence is strictly growing, even though A329902 (whose subsequence this is) is not monotonic.
Conjectured to be a subsequence of A330745.

Antti Karttunen, Table of n, a(n) for n = 1..223 (computed from the 10000 term b-file of A002182 prepared from Flammenkamp's data)

Cf. A002182, A108951, A133411, A329900, A329902, A330745.

PARI
```
A330744(n) = A329900(A133411(n));
```

a(n) = A329900(A133411(n)).

A354880 Numbers k where A133411(k) is not equal to A328521(k-1).

Original entry on oeis.org

17, 19, 21, 51, 52, 55, 56, 57, 58, 59, 60, 61, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 127, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169

Offset: 1

J. Lowell, Jun 09 2022

nonn

			A133411(17)=5587021440. (5587021440/19 = A133411(16) = 294053760.) But A328521(16)=2205403200. (2205403200 has 16 prime factors and is A328521(16) even if not 294053760 times an integer [the quotient is 15/2].) Thus, 17 is a term of this sequence.

Cf. A133411, A328521.

A351627 a(n) = A133411(n+1)/A133411(n).

Original entry on oeis.org

2, 2, 3, 2, 2, 5, 3, 7, 2, 2, 11, 3, 13, 2, 17, 19, 5, 23, 3, 7, 2, 29, 31, 2, 37, 5, 41, 43, 47, 2, 53, 11, 59, 61, 3, 67, 71, 3, 73, 13, 79, 83, 89, 5, 97, 101, 103, 7, 107, 109, 113, 17, 127, 131, 19, 137, 139, 149, 151, 2, 2, 157, 163, 167, 173, 179, 181, 23

Offset: 1

J. Lowell, May 04 2022

nonn

Conjecture: all terms are prime numbers.

			221760/20160 = 11, so a(11)=11.

Cf. A133411.

More terms from Amiram Eldar, May 04 2022

A328521 Smallest highly composite number that has n prime factors counted with multiplicity.

Original entry on oeis.org

1, 2, 4, 12, 24, 48, 240, 720, 5040, 10080, 20160, 221760, 665280, 8648640, 17297280, 294053760, 2205403200, 27935107200, 293318625600, 1927522396800, 8995104518400, 26985313555200, 782574093100800, 24259796886124800, 48519593772249600, 1795224969573235200, 8976124847866176000, 368021118762513216000

Offset: 0

David A. Corneth, Jan 04 2020

nonn

a(n-1) differs from A133411(n) for n in A354880.

Question: Is this sequence strictly growing? If sequence A330748 is monotonic, so is this also, and vice versa. Note that the primorial deflation sequence, A330743, is not monotonic. - Antti Karttunen, Jan 14 2020

Amiram Eldar, Table of n, a(n) for n = 0..394

Cf. A001222 (bigomega), A002182 (highly composite numbers), A108951, A112778 (bigomega of HCN's), A330743 (primorial deflation), A330748 (indices in A002182).
Cf. also A133411.
Cf. A354880.

(* First load the function f at A025487, then: *)
Block[{s = Union@ Flatten@ f@ 17, t}, t = DivisorSigma[0, s]; s = Map[s[[FirstPosition[t, #][[1]] ]] &, Union@ FoldList[Max, t]]; t = PrimeOmega[s]; Array[s[[FirstPosition[t, #][[1]] ]] &, Max@ t + 1, 0]] (* Michael De Vlieger, Jan 12 2020 *)

a(n)=for(k=1,oo,bigomega(A2182[k])==n&&return(A2182[k])) \\ Global variable A2182 must hold a vector of values of A002182. - M. F. Hasler, Jan 08 2020

a(n) = A002182(A330748(n)) = A002182(min{k: A112778(k)=n}). - M. F. Hasler, Jan 08 2020

a(n) = A108951(A330743(n)), where A330743(n) is the first term k of A329902 for which A056239(k) = n. - Antti Karttunen, Jan 13 2020

cp's OEIS Frontend

A330744 Primorial deflation of A133411(n), where A133411(n) is the smallest highly composite number of the form k*a(n-1) where k is an integer greater than 1.

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A354880 Numbers k where A133411(k) is not equal to A328521(k-1).

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A351627 a(n) = A133411(n+1)/A133411(n).

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A328521 Smallest highly composite number that has n prime factors counted with multiplicity.

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