|
Search: id:A117582
|
|
|
| A117582 |
|
For successive primes p, the number of ratios of the form n^2/(n^2-1) which factor into primes less than or equal to p. |
|
+0
3
|
|
| 0, 2, 5, 10, 15, 24, 34, 46, 57, 74, 90, 114, 141
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
By a theorem of Stormer, the number of ratios m/(m-1) factoring into primes only up to p is finite. A proportion of these have square denominators.
|
|
REFERENCES
|
E. F. Ecklund and R. B. Eggleton, Prime factors of consecutive integers, Amer. Math. Monthly, 79 (1972), 1082-1089.
D. H. Lehmer, On a problem of Stormer, Ill. J. Math., 8 (1964), 57-69.
|
|
CROSSREFS
|
Cf. A002071, A117583.
Sequence in context: A013927 A163059 A099738 this_sequence A002134 A062472 A086849
Adjacent sequences: A117579 A117580 A117581 this_sequence A117583 A117584 A117585
|
|
KEYWORD
|
hard,nonn
|
|
AUTHOR
|
Gene Ward Smith (genewardsmith(AT)gmail.com), Apr 02 2006
|
|
|
Search completed in 0.003 seconds
|
