login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A259939 Smallest Product_{i:lambda} prime(i) for any perfect partition lambda of n. 3
1, 2, 4, 6, 16, 18, 64, 42, 100, 162, 1024, 234, 4096, 1088, 1936, 798, 65536, 2300, 262144, 4698, 18496, 31744, 4194304, 8658, 234256, 167936, 52900, 46784, 268435456, 90992, 1073741824, 42294, 984064, 3866624, 5345344, 140300, 68719476736, 17563648, 6885376 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
A perfect partition of n contains a unique partition for any k in {0,...,n}. See also A002033.
LINKS
Eric Weisstein's World of Mathematics, Perfect Partition
FORMULA
a(n) = A258119(n,1).
EXAMPLE
For n=7 there are 4 perfect partitions: [4,1,1,1], [4,2,1], [2,2,2,1] and [1,1,1,1,1,1,1], their encodings as Product_{i:lambda} prime(i) give 56, 42, 54, 128, respectively. The smallest value is a(7) = 42.
MAPLE
b:= (n, l)-> `if`(n=1, 2^(l[1]-1)*mul(ithprime(mul(l[j],
j=1..i-1))^(l[i]-1), i=2..nops(l)), min(seq(b(n/d,
[l[], d]), d=numtheory[divisors](n) minus{1}))):
a:= n-> `if`(n=0, 1, b(n+1, [])):
seq(a(n), n=0..42);
MATHEMATICA
b[n_, l_] := If[n==1, 2^(l[[1]]-1)*Product[Prime[Product[l[[j]], {j, 1, i-1}]]^(l[[i]]-1), {i, 2, Length[l]}], Min[Table[b[n/d, Append[l, d]], {d, Divisors[n] ~Complement~ {1}}]]];
a[n_] := If[n==0, 1, b[n+1, {}]];
Table[a[n], {n, 0, 42}] (* Jean-François Alcover, Mar 23 2017, translated from Maple *)
CROSSREFS
Column k=1 of A258119.
Sequence in context: A333021 A114874 A100361 * A069654 A330359 A000068
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 09 2015
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)