

A061112


a(n) is the minimum number of divisors for any composite between prime(n) and prime(n+1).


3



3, 4, 3, 6, 4, 6, 4, 3, 8, 4, 4, 8, 4, 3, 4, 12, 4, 4, 12, 4, 4, 4, 4, 6, 8, 4, 12, 4, 3, 4, 4, 8, 4, 12, 4, 4, 4, 3, 4, 18, 4, 14, 4, 12, 4, 4, 4, 12, 8, 4, 20, 4, 4, 4, 4, 16, 4, 4, 8, 3, 4, 4, 16, 4, 4, 4, 4, 12, 8, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 24, 4, 20, 4, 8, 4, 4, 4, 16, 4, 4, 4, 4, 4, 4, 4, 4
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OFFSET

2,1


LINKS

Harry J. Smith, Table of n, a(n) for n = 2..1000.


FORMULA

a(n) = Min_{c=prime(n)+1..prime(n+1)1} tau(c) where tau(c) is the number of divisors of c.


EXAMPLE

p(30)=113 is followed by 13 composites; their numbers of divisors are {8, 4, 6, 6, 4, 4, 16, 3, 4, 4, 6, 4, 12}. The smallest is 3, so a(30)=3. [corrected by Jon E. Schoenfield, Sep 20 2022]


PROG

(PARI) { n=1; q=3; m=10^6; forprime (p=5, prime(1003), a=m; for (i=q + 1, p  1, a=min(numdiv(i), a)); q=p; write("b061112.txt", n++, " ", a) ) } \\ Harry J. Smith, Jul 19 2009


CROSSREFS

Cf. A000005, A061117.
Sequence in context: A338128 A242801 A021295 * A078809 A245218 A097857
Adjacent sequences: A061109 A061110 A061111 * A061113 A061114 A061115


KEYWORD

nonn


AUTHOR

Labos Elemer, May 29 2001


STATUS

approved



