|
| |
|
|
A241813
|
|
Numbers disqualified from being in A019505 for not being the smallest number with their respective number of divisors.
|
|
0
|
|
|
|
8, 96, 480, 1440, 40320, 443520, 1330560, 34594560, 86486400, 588107520, 1470268800, 11174042880, 55870214400, 195545750400, 1285014931200, 17990209036800, 53970627110400, 1565148186201600, 194078375088998400, 7180899878292940800, 35904499391464704000, 294416895010010572800
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
It appears that when 2*A019505(n) is a member of this sequence then the exponent in at least one primary of the factorization of A019505(n+1) is smaller than in the corresponding primary of A019505(n) or A019505(n+1) contains an additional prime factor. The smallest example in this sequence where two primaries have smaller exponents and an additional prime factor is added is a(14) = 2*A019505(43) = 2 * 97772875200 = 195545750400. The sequence of exponents of its primaries is (7, 3, 2, 2, 1, 1, 1, 1 ) while A019505(44) = 160626866400 has exponent sequence (5, 3, 2, 1, 1, 1, 1, 1, 1 ). - Hartmut F. W. Hoft, Feb 22 2023
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
8 qualifies because 8 = 4*2 and 4 is in A019505, but 8 can't be term after 4 in A019505 because smallest number with 4 divisors is 6.
|
|
|
MATHEMATICA
|
dataA019505 = Map[Last, Import[URL["https://oeis.org/A019505/b019505.txt"], "Data"]]
dataA241813 = Take[Map[First, Select[Map[{2#[[1]], 2#[[1]]==#[[2]]}&, Transpose[{Most[dataA019505], Rest[dataA019505]}]], !#[[2]]&]], 22] (* Hartmut F. W. Hoft, Feb 22 2023 *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,more
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
