A330744 -id:A330744 - cp's OEIS frontend

A133411 Smallest highly composite number of the form k*a(n-1) where k is an integer greater than 1.

1, 2, 4, 12, 24, 48, 240, 720, 5040, 10080, 20160, 221760, 665280, 8648640, 17297280, 294053760, 5587021440, 27935107200, 642507465600, 1927522396800, 13492656777600, 26985313555200, 782574093100800, 24259796886124800

Offset: 1

J. Lowell, Nov 25 2007

nonn

Conjecture: subsequence of A019505.

			6 is not in the sequence because 6 is not a multiple of 4, the previous term.

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, A019505, A328521, A330744 (primorial deflation).

sublist_of_first_proper_multiple_terms_of(v) = { my(u=v[1], lista=List(u)); for(i=2,#v,if((v[i]>u)&&!(v[i]%u), u = v[i]; listput(lista,u))); Vec(lista); };
v133411 = sublist_of_first_proper_multiple_terms_of(v002182); \\ v002182 contains the terms of A002182.
A133411(n) = v133411[n]; \\ Antti Karttunen, Jan 10 2020

a(12)-a(24) from Donovan Johnson, Sep 09 2008

A330743 a(n) is the first term k of A329902 for which A056239(k) = n.

Original entry on oeis.org

1, 2, 4, 6, 12, 24, 40, 60, 84, 168, 336, 528, 792, 936, 1872, 2448, 3060, 4560, 4788, 8280, 15456, 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: 0

Antti Karttunen, Jan 13 2020

nonn

Note that in contrast to A330744 this is not monotonic. The first point where a(n) > a(n+1) occurs is at a(120) = 5481774144 > a(121) = 5452302240. See also comment in A328521, whose primorial deflation this sequence is.

a(n-1) differs from A330744(n) at n = 17, 19, 21, 51, 52, 55, 56, 57, 58, 59, 60, 61, ...

Antti Karttunen, Table of n, a(n) for n = 0..4257

Primorial deflation of A328521.
Cf. A056239, A319626, A329900, A329902, A330748.
Cf. also A330744.

A330743(n) = { for(k=1,oo,if(A056239(A329902(k))==n,return(A329902(k)))); };

v329902 = readvec("a329902.txt"); \\ File for the first 779674 terms of A329902 as prepared by Michael De Vlieger.
A056239(n) = if(1==n,0,my(f=factor(n)); sum(i=1, #f~, f[i,2] * primepi(f[i,1])));
A330743list() = { my(m=Map(), lista=List([]), t); for(i=1, #v329902, t = A056239(v329902[i]); if(!mapisdefined(m,t), mapput(m,t,v329902[i]))); for(n=0,oo,if(mapisdefined(m,n,&t), listput(lista,t), return(Vec(lista)))); };
v330743 = A330743list();
A330743(n) = v330743[1+n];
for(n=0,#v330743-1,write("b330743.txt", n, " ", A330743(n)));

a(n) = A329902(min{i: A056239(A329902(i))==n}).
a(n) = A329902(A330748(n)).
a(n) = A329900(A328521(n)) = A319626(A328521(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

A133411 Smallest highly composite number of the form k*a(n-1) where k is an integer greater than 1.

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A330743 a(n) is the first term k of A329902 for which A056239(k) = 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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