|
|
A353264
|
|
a(n) is the least number k such that A018804(k)/k = n.
|
|
0
|
|
|
1, 4, 15, 64, 48, 60, 144, 16384, 240, 1300, 1296, 960, 1008, 3564, 3840, 1073741824, 6000, 14580, 7056, 20800, 11520, 25500, 944784, 245760, 13104, 24948, 34560, 57024, 750000, 16380, 156816, 4611686018427387904, 102000, 364500, 46800, 233280, 134064, 174636
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
a(n) exist for all n>=1.
The solution k to A018804(k)/k = n is unique if and only if n is a power of 2: a(2^m) = 2^(2^(m+1)-2) = A051191(m+1).
The questions of existence and uniqueness are a part of a problem that was proposed during the Forty-Fifth International Mathematical Olympiad in Athens, Greece, July 7-19, 2004.
|
|
REFERENCES
|
Dušan Djukić, Vladimir Janković, Ivan Matić, and Nikola Petrović, The IMO Compendium, A Collection of Problems Suggested for the International Mathematical Olympiads: 1959-2004, Springer, New York, 2006. See Problem 25, pp. 331, 726-727.
|
|
LINKS
|
Dušan Djukić, Vladimir Janković, Ivan Matić, and Nikola Petrović, IMO Shortlist 2004, 2005, Problem 25, pp. 5-6, 18-19.
R. E. Woodrow, Problem N2, The Olympiad Corner, Crux Mathematicorum, Vol. 34, No. 7 (2008), pp. 419-421.
|
|
EXAMPLE
|
a(2) = 4 since A018804(4)/4 = 8/4 = 2 and 4 is the least number with this property.
|
|
MATHEMATICA
|
f[p_, e_] := (e*(p - 1)/p + 1); r[n_] := Times @@ (f @@@ FactorInteger[n]); a[n_] := Module[{k = 1}, While[r[k] != n, k++]; k]; Array[a, 15]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|