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Maximum number of divisors for any composite between prime(n) and prime(n+1).
3

%I #13 Jul 02 2018 01:42:31

%S 3,4,4,6,5,6,6,8,8,9,8,8,6,10,8,12,8,8,12,8,10,12,12,9,8,8,12,10,16,8,

%T 12,8,15,12,12,12,8,16,10,18,8,14,9,12,16,16,12,12,8,12,20,8,18,12,16,

%U 16,12,16,8,18,18,12,16,12,16,20,12,12,12,8,24,12,16,12,16,18,15,16,12

%N Maximum number of divisors for any composite between prime(n) and prime(n+1).

%H Michael De Vlieger, <a href="/A061117/b061117.txt">Table of n, a(n) for n = 2..10000</a> (terms up to n = 1000 by Harry J. Smith)

%F a(n) = Max{d(c); p(n+1) > c > p(n)}, c is composite, p(n) is the n-th prime and d=A000005().

%e p(30)=113 is followed by 13 composites; numbers of divisors are {8, 4, 6, 6, 4, 4, 16, 3, 4, 4, 6, 4, 12}; the smallest is 4=a(30) and the largest is 16.

%t Max /@ DivisorSigma[0, Select[SplitBy[Range@ Prime@ 81, PrimeQ], CompositeQ@ First@ # &]] (* _Michael De Vlieger_, Nov 02 2017 *)

%o (PARI) { n=-1; q=3; forprime (p=5, prime(1003), a=0; for (i=q + 1, p - 1, a=max(numdiv(i), a)); q=p; write("b061117.txt", n++, " ", a) ) } \\ _Harry J. Smith_, Jul 18 2009

%Y Cf. A000005, A061112.

%K nonn

%O 2,1

%A _Labos Elemer_, May 29 2001