|
Search: id:A143346
|
|
|
| A143346 |
|
The number of distinct prime factors occurring in the numbers between n^2 and (n+1)^2. |
|
+0
1
|
|
| 2, 4, 6, 8, 9, 12, 13, 14, 17, 18, 20, 22, 23, 26, 25, 29, 30, 32, 33, 36, 37, 37, 41, 42, 44, 45, 45, 51, 49, 53, 54, 53, 58, 57, 62, 62, 65, 63, 66, 70, 70, 72, 73, 74, 78, 77, 79, 84, 81, 86, 85, 90, 87, 93, 93, 94, 97, 99, 99, 100, 102, 105, 105, 109, 109, 109, 115, 111
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Same as the number of distinct prime factors in (2n^2+2n)!/(n^2)!. The plot appears nearly linear.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=1..10000
|
|
EXAMPLE
|
The numbers between 4 and 9 have factorizations 5, 2*3, 7, 2^4, which use primes 2, 3, 5 and 7. Hence a(2)=4.
|
|
MATHEMATICA
|
Table[a=n^2; b=a+2*n; Sum[Sign[Quotient[b, p]-Quotient[a, p]], {p, Prime[Range[PrimePi[b]]]}], {n, 100}]
|
|
CROSSREFS
|
Cf. A014085 (number of primes between n^2 and (n+1)^2).
Sequence in context: A114571 A050091 A047294 this_sequence A138969 A161819 A071562
Adjacent sequences: A143343 A143344 A143345 this_sequence A143347 A143348 A143349
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
T. D. Noe (noe(AT)sspectra.com), Aug 09 2008
|
|
|
Search completed in 0.002 seconds
|
