OFFSET
1,14
COMMENTS
This sequence first differs from sequence A117371 at the 30th term.
Records in a(n) are for n = 2*prime(k), for which a(n) = k-2. Examples: a(14) = a(2*prime(4)) = 4-2 = 2; a(22) = a(2*prime(5)) = 5-2 = 3; a(26) = a(2*prime(6)) = 6-2 = 4; a(74) = a(2*prime(12)) = 12-2= 10. Those records are each repeated for n = 2*(prime(k)^e_1)*(prime(m)^e_2)*(prime(n)^e_3)...*(prime(x)^e_y) where e_i are positive integers and prime(m), ..., prime(x) are between 2 and prime(k). Minima a(n) = 0 iff least spf(n)=gpf(n) iff n is 1 or a prime power (A000961), or a product of powers of consecutive primes (prime(k)^e_1)*(prime(k+1)^e_2). Here gpf(n) = greatest prime factor = A006530(n) and spf(n) = smallest prime factor = A020639(n). - Jonathan Vos Post, Mar 11 2006
LINKS
FORMULA
If A001221(n)<=1, a(n) = 0, otherwise a(n) = A243055(n) - 1 = (A061395(n)-A055396(n))-1. - Antti Karttunen, Sep 10 2018
EXAMPLE
a(30) is 1 because there is one prime (which is 3) between the smallest prime dividing 30 (which is 2) and the largest prime dividing 30 (which is 5).
PROG
(PARI) A117370(n) = if(1>=omega(n), 0, my(f = factor(n), lpf = f[1, 1], gpf = f[#f~, 1]); -1+(primepi(gpf)-primepi(lpf))); \\ Antti Karttunen, Sep 10 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Mar 10 2006
EXTENSIONS
More terms from Jonathan Vos Post, Mar 11 2006
More terms from Franklin T. Adams-Watters, Aug 29 2006
STATUS
approved