|
| |
|
|
A117371
|
|
Number of primes between smallest prime divisor of n and largest prime divisor of n which are coprime to n.
|
|
2
| |
|
|
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 5, 0, 0, 0, 6, 3, 1, 0, 1, 0, 3, 0, 7, 0, 0, 0, 1, 4, 4, 0, 0, 1, 2, 5, 8, 0, 0, 0, 9, 1, 0, 2, 2, 0, 5, 6, 1, 0, 0, 0, 10, 0, 6, 0, 3, 0, 1, 0, 11, 0, 1, 3, 12, 7, 3, 0, 0, 1, 7, 8, 13, 4, 0, 0, 2, 2, 1, 0, 4, 0
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,14
|
|
|
COMMENTS
| This sequence first differs from sequence A117370 at the 30th term.
|
|
|
EXAMPLE
| a(30) is 0 because the one prime (which is 3) between the smallest prime dividing 30 (which is 2) and the largest prime dividing 30 (which is 5) is not coprime to 30. On the other hand, a(14) = 2 because there are two primes (3 and 5) which are between 14's least prime divisor (2) and greatest prime divisor (7) and 3 and 5 are both coprime to 14.
|
|
|
MAPLE
| A020639 := proc(n) local ifs; if n = 1 then 1 ; else ifs := ifactors(n)[2] ; min(seq(op(1, i), i=ifs)) ; fi ; end: A006530 := proc(n) local ifs; if n = 1 then 1 ; else ifs := ifactors(n)[2] ; max(seq(op(1, i), i=ifs)) ; fi ; end: A117371 := proc(n) local a, i ; a := 0 ; if n < 2 then 0 ; else for i from A020639(n)+1 to A006530(n)-1 do if isprime(i) and gcd(i, n) = 1 then a := a+1 ; fi ; od; fi ; RETURN(a) ; end: seq(A117371(n), n=1..140) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 05 2007
|
|
|
CROSSREFS
| Cf. A117370.
Sequence in context: A188172 A106671 A033776 * A117370 A151756 A112053
Adjacent sequences: A117368 A117369 A117370 * A117372 A117373 A117374
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Leroy Quet, Mar 10 2006
|
|
|
EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 05 2007
|
| |
|
|
