%I A117370
%S A117370 0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,0,0,0,0,1,1,3,0,0,0,4,0,2,0,1,0,0,2,5,0,
%T A117370 0,0,6,3,1,0,2,0,3,0,7,0,0,0,1,4,4,0,0,1,2,5,8,0,1,0,9,1,0,2,3,0,5,6,2,
%U A117370 0,0,0,10,0,6,0,4,0,1,0,11,0,2,3,12,7,3,0,1,1,7,8,13,4,0,0,2,2,1,0,5,0
%N A117370 Number of primes between smallest prime divisor of n and largest prime
divisor of n.
%C A117370 This sequence first differs from sequence A117371 at the 30th term.
%C A117370 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 (jvospost3(AT)gmail.com), Mar 11 2006
%H A117370 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a>
(listed in lieu of email address)
%e A117370 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).
%Y A117370 Cf. A117371.
%Y A117370 Cf. A000961, A006530, A020639.
%Y A117370 Sequence in context: A106671 A033776 A117371 this_sequence A151756 A112053
A089798
%Y A117370 Adjacent sequences: A117367 A117368 A117369 this_sequence A117371 A117372
A117373
%K A117370 nonn
%O A117370 1,14
%A A117370 Leroy Quet, Mar 10 2006
%E A117370 More terms from Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 11 2006
%E A117370 More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Aug 29
2006
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