

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
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OFFSET

1,14


COMMENTS

This sequence first differs from sequence A117370 at the 30th term.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537


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

Cf. A117370, A137795.
Sequence in context: A188172 A106671 A033776 * A117370 A309395 A260943
Adjacent sequences: A117368 A117369 A117370 * A117372 A117373 A117374


KEYWORD

nonn


AUTHOR

Leroy Quet, Mar 10 2006


EXTENSIONS

More terms from R. J. Mathar, Sep 05 2007


STATUS

approved



