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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 7 09:17 EDT 2022. Contains 357270 sequences. (Running on oeis4.)