|
|
A076446
|
|
Differences of consecutive powerful numbers (definition 1).
|
|
5
|
|
|
3, 4, 1, 7, 9, 2, 5, 4, 13, 15, 8, 9, 19, 8, 13, 4, 3, 16, 25, 27, 4, 16, 9, 18, 13, 32, 1, 35, 19, 18, 31, 8, 32, 9, 43, 16, 12, 17, 47, 49, 23, 27, 1, 53, 55, 16, 41, 23, 36, 61, 7, 4, 28, 24, 65, 36, 27, 4, 69, 71, 27, 8, 21, 17, 3, 72, 77, 47, 32, 81, 47, 36, 36, 49, 87, 8
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The term 1 appears infinitely often. Erdos conjectured that two consecutive 1's do not occur. (see Guy).
|
|
REFERENCES
|
R. K. Guy, Unsolved Problems in Number Theory, B16
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
The first two powerful numbers are 1 and 4, there difference is 3, so a(1)=3.
|
|
MATHEMATICA
|
Differences[Join[{1}, Select[Range[2000], Min[FactorInteger[#][[All, 2]]]>1&]]] (* Harvey P. Dale, Aug 27 2017 *)
|
|
PROG
|
(Haskell)
a076446 n = a076446_list !! (n-1)
a076446_list = zipWith (-) (tail a001694_list) a001694_list
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|