|
Search: id:A063528
|
|
|
| A063528 |
|
Smallest number such that it and its successor are both divisible by an n-th power larger than 1. |
|
+0
10
|
|
| 2, 8, 80, 80, 1215, 16767, 76544, 636416, 3995648, 24151040, 36315135, 689278976, 1487503359, 1487503359, 155240824832, 785129144319, 4857090670592, 45922887663615, 157197025673216, 1375916505694208
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Lesser of the smallest pair of consecutive numbers divisible by an n-th power.
To get a(j), max exponent[=A051953(n)] of a(j) and 1+a(j) should exceed (j-1).
|
|
REFERENCES
|
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 242, p. 67, Ellipses, Paris 2008.
|
|
EXAMPLE
|
a[4]=80 since 2^4=16 divides 80 and 3^4=81 divides 81
|
|
MATHEMATICA
|
k = 4; Do[k = k - 2; a = b = 0; While[ b = Max[ Transpose[ FactorInteger[k]] [[2]]]; a <= n || b <= n, k++; a = b]; Print[k - 1], {n, 0, 19} ]
|
|
CROSSREFS
|
We need A051903(a[n]) > n-1 and A051903(a[n]+1) > n-1.
Cf. A068780, A068781, A068140, A068782, A068783, A068784.
Cf. A045330, A059737.
Sequence in context: A093062 A057984 A071254 this_sequence A073561 A130530 A134529
Adjacent sequences: A063525 A063526 A063527 this_sequence A063529 A063530 A063531
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Erich Friedman (efriedma(AT)stetson.edu), Aug 01 2001
|
|
EXTENSIONS
|
More terms from Jud McCranie (j.mccranie(AT)comcast.net), Aug 06 2001
|
|
|
Search completed in 0.002 seconds
|
