|
| |
|
|
A117371
|
|
Number of primes between smallest prime divisor of n and largest prime divisor of n that are coprime to n (not factors of 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;
text;
internal format)
|
|
|
|
OFFSET
|
1,14
|
|
|
COMMENTS
|
This sequence first differs from sequence A117370 at the 30th term.
|
|
|
LINKS
|
|
|
|
FORMULA
|
|
|
|
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) that 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, Sep 05 2007
|
|
|
MATHEMATICA
|
Table[Count[Prime[Range[PrimePi@ First@ # + 1, PrimePi@ Last@ # - 1]], _?(GCD[#, n] == 1 &)] &@ FactorInteger[n][[All, 1]], {n, 103}] (* Michael De Vlieger, Sep 10 2018 *)
|
|
|
PROG
|
(PARI) A117371(n) = if(1==n, 0, my(f = factor(n), p = f[1, 1], gpf = f[#f~, 1], c = 0); while(p<gpf, if((n%p), c++); p = nextprime(1+p)); (c)); \\ Antti Karttunen, Sep 10 2018
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
