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a(n) = the minimum of d(p(n)-1) and d(p(n)+1), where d(m) is the number of divisors of m and p(n) is the n-th prime.
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%I #14 Sep 28 2018 15:20:47

%S 1,2,3,4,4,4,5,6,4,6,6,4,8,6,4,6,4,4,6,8,4,8,4,8,6,8,8,4,8,8,8,8,8,8,

%T 6,8,4,6,4,6,4,8,8,4,9,12,6,8,4,8,8,8,6,8,8,4,6,10,4,8,6,6,12,8,4,6,6,

%U 6,4,12,8,4,8,8,12,4,6,4,8,8,8,4,8,8,8,8,14,4,12,10,4,4,8,12,8,4,6,12,6,4,6

%N a(n) = the minimum of d(p(n)-1) and d(p(n)+1), where d(m) is the number of divisors of m and p(n) is the n-th prime.

%t Table[Min[DivisorSigma[0, Prime[n]-1], DivisorSigma[0, Prime[n]+1]], {n, 1, 100}] (* _Stefan Steinerberger_, Oct 11 2008 *)

%o (PARI) a(n) = my(p = prime(n)); min(numdiv(p-1), numdiv(p+1)); \\ _Michel Marcus_, Sep 28 2018

%Y Cf. A145340, A008328, A008329, A067889, A103664, A103665.

%K nonn

%O 1,2

%A _Leroy Quet_, Oct 08 2008

%E More terms from _Stefan Steinerberger_ and _Ray Chandler_, Oct 11 2008