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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
OFFSET
1,14
COMMENTS
This sequence first differs from sequence A117370 at the 30th term.
LINKS
FORMULA
a(n) = A001221(A137795(n)). - Antti Karttunen, Sep 10 2018
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
Sequence in context: A188172 A106671 A033776 * A117370 A332007 A309395
KEYWORD
nonn
AUTHOR
Leroy Quet, Mar 10 2006
EXTENSIONS
More terms from R. J. Mathar, Sep 05 2007
STATUS
approved