A329902 -id:A329902 - 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)).

A330748 Index of the smallest element in A002182 that has exactly n prime factors counted with multiplicity.

Original entry on oeis.org

1, 2, 3, 5, 6, 8, 12, 14, 19, 21, 23, 32, 37, 47, 50, 62, 70, 80, 91, 99, 105, 109, 124, 140, 143, 159, 166, 182, 198, 217, 221, 240, 253, 276, 297, 304, 327, 352, 357, 381, 398, 424, 449, 475, 485, 512, 540, 570, 584, 617, 642, 676, 704, 738, 765, 770, 805, 841, 877, 913, 937, 949, 985, 1021, 1058, 1096, 1134, 1169

Offset: 0

Antti Karttunen, suggested by M. F. Hasler, Jan 10 2020

nonn

Michael De Vlieger, Table of n, a(n) for n = 0..4257 (computed using A. Flammenkamp's 779674-term HCN dataset; terms 0..329 from _Antti Karttunen_)

Cf. A001222, A002182, A112778, A328521, A329902, A330743.

A330748(n) = { for(k=1,#v112778,if(v112778[k]==n,return(k))); -(1/0); };

v329902 = readvec("a329902.txt"); \\ File for the first 779674 terms of A329902
A056239(n) = if(1==n,0,my(f=factor(n)); sum(i=1, #f~, f[i,2] * primepi(f[i,1])));
A330748list() = { my(m=Map(), lista=List([]), t); for(i=1, #v329902, t = A056239(v329902[i]); if(!mapisdefined(m,t), mapput(m,t,i))); for(n=0,oo,if(mapisdefined(m,n,&t), listput(lista,t), return(Vec(lista)))); };
v330748 = A330748list();
A330748(n) = v330748[1+n];
for(n=0,#v330748-1,write("b330748.txt", n, " ", A330748(n))); \\ Antti Karttunen, Jan 13 2020

a(n) = min{k: A112778(k)=n}.
A002182(a(n)) = A328521(n).
A329902(a(n)) = A330743(n).

A353562 Prime shadows of highly composite numbers, A002182.

Original entry on oeis.org

1, 2, 3, 4, 6, 10, 9, 14, 12, 20, 18, 28, 30, 42, 40, 36, 56, 60, 84, 100, 132, 140, 156, 126, 120, 196, 198, 168, 200, 264, 280, 312, 252, 440, 392, 396, 520, 336, 400, 528, 560, 624, 504, 880, 784, 792, 1040, 840, 936, 1360, 1320, 1176, 1120, 1560, 1008, 1760, 1568, 1584, 2080, 1680, 1872, 2720, 2640, 2352, 2240, 3120

Offset: 1

Antti Karttunen, Apr 29 2022

nonn

Sequence is injective (no duplicate values occur) because A002182 is a subsequence of A025487.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A002182, A025487, A122111, A181819, A329902.

Cf. also A353561, A353568.

v002182 = readvec("b002182_to.txt"); \\ Prepared from b-file of A002182 with gawk ' { print $2 } '
A002182(n) = v002182[n];
A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
A353562(n) = A181819(A002182(n));

a(n) = A181819(A002182(n)).

a(n) = A122111(A329902(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)).

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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A330748 Index of the smallest element in A002182 that has exactly n prime factors counted with multiplicity.

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A353562 Prime shadows of highly composite numbers, A002182.

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

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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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