A329900 -id:A329900 - 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)).

A329889 a(n) is the unique integer k such that A108951(k) = A260633(n).

Original entry on oeis.org

1, 3, 6, 12, 5, 10, 20, 15, 30, 60, 28, 45, 21, 56, 90, 42, 180, 84, 63, 168, 70, 126, 140, 252, 189, 280, 504, 210, 378, 264, 1008, 420, 315, 220, 840, 630, 1680, 792, 330, 1260, 1584, 945, 1400, 660, 2520, 495, 1890, 882, 1320, 2100, 990, 1764, 2640, 4200, 1980, 3528, 1485, 2200, 8400, 2646, 3960, 6300, 2970, 5292, 7920, 3300, 5940, 2772

Offset: 1

Antti Karttunen, Dec 28 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 1..2011 (computed from the b-file of A260633)

Cf. A008480, A050382, A108951, A260633, A329900.

Cf. also A329902, A330686.

a(n) = A329900(A260633(n)).

A330684 Square roots of the positions of records in A050377, number of ways to factor n into "Fermi-Dirac primes" (A050376).

Original entry on oeis.org

1, 2, 4, 8, 12, 16, 24, 32, 36, 48, 72, 96, 144, 288, 432, 576, 864, 1152, 1440, 1728, 2304, 2880, 4320, 4608, 5184, 5760, 6912, 7200, 8640, 10368, 11520, 14400, 20736, 23040, 25920, 28800, 34560, 41472, 43200, 51840, 57600, 82944, 86400, 100800, 103680, 115200, 129600, 172800, 207360, 230400, 259200, 345600, 388800, 403200

Offset: 1

Antti Karttunen, Dec 29 2019

nonn

Like terms in A330687, also these are all found in A025487.

Antti Karttunen, Table of n, a(n) for n = 1..1004 (computed from the b-file David A. Corneth computed for A330687)

Cf. A000196, A050376, A050377, A108951, A329900, A330687, A330689.

Subsequence of A025487.

PARI
```
A330684(n) = sqrtint(A330687(n));
```

a(n) = A000196(A330687(n)).
A108951(a(n)) = A000196(A330689(n)).
a(n) = A329900(A000196(A330689(n))).

A330685 Primorial deflation of highly factorable numbers: a(n) is the unique integer x such that A108951(x) = A033833(n).

Original entry on oeis.org

1, 4, 8, 6, 16, 12, 9, 24, 18, 48, 20, 36, 96, 27, 40, 72, 30, 54, 80, 144, 60, 160, 45, 288, 120, 90, 240, 180, 84, 480, 200, 360, 168, 960, 270, 400, 126, 720, 336, 540, 800, 252, 1440, 672, 280, 1080, 504, 1344, 378, 560, 1008, 420, 2688, 2400, 756, 1120, 2016, 840, 1512, 630, 4032, 1680, 3024, 1260, 2268, 3360, 6048, 2520, 4536, 6720

Offset: 1

Antti Karttunen, Dec 28 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 1..235 (computed from the b-file of A033833)

Cf. A001055, A028422, A033833, A108951, A329900.

a(n) = A329900(A033833(n)).

A330745 Primorial deflation of A019505(n), where A019505(n) is smallest number with same number of divisors as 2*A019505(n-1), starting from A019505(1) = 1.

Original entry on oeis.org

1, 2, 4, 3, 6, 12, 24, 10, 20, 40, 30, 60, 21, 42, 84, 168, 336, 66, 132, 264, 528, 396, 792, 117, 234, 468, 936, 1872, 780, 1560, 612, 1224, 2448, 1020, 2040, 684, 1368, 2736, 1140, 2280, 4560, 1596, 3192, 1380, 2760, 5520, 1932, 3864, 7728, 15456, 11592, 23184, 1827, 3654, 7308, 14616, 29232, 1953, 3906, 7812, 15624, 31248, 62496

Offset: 1

Antti Karttunen, Jan 10 2020

nonn

a(n) is the unique integer k such that A108951(k) = A019505(n).
Conjectured to be a subsequence of A329902.
Terms computed from b-file of A019505 provided by R. J. Mathar.

Cf. A019505, A108951, A329900, A329902.

Cf. A330744 (conjectured subsequence).

PARI
```
A330745(n) = A329900(A019505(n));
```

a(n) = A329900(A019505(n)).

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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A329889 a(n) is the unique integer k such that A108951(k) = A260633(n).

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A330684 Square roots of the positions of records in A050377, number of ways to factor n into "Fermi-Dirac primes" (A050376).

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A330685 Primorial deflation of highly factorable numbers: a(n) is the unique integer x such that A108951(x) = A033833(n).

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Author

Keywords

Links

Crossrefs

Formula

A330745 Primorial deflation of A019505(n), where A019505(n) is smallest number with same number of divisors as 2*A019505(n-1), starting from A019505(1) = 1.

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Author

Keywords

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Programs

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Formula