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%I #14 Oct 28 2023 14:35:30
%S 1,2,2,4,2,2,4,8,8,4,4,16,2,4,8,8,4,8,8,4,4,16,8,2,4,4,16,16,16,8,8,8,
%T 8,8,8,16,16,16,32,8,32,16,32,16,16,16,16,4,8,8,4,16,8,16,4,16,16,128,
%U 16,8,8,16,16,8,8,2,8,2,16,8,32,32,16,16,64,32
%N The number of divisors of prime(n)#-1 where p# is the product of all the primes from 2 to p inclusive.
%F a(n) = sigma0(prime(n)#-1) = A000005(A057588(n)).
%e a(4)=4 because the divisors of 7#-1 = 209 are {1, 11, 19, 209}.
%p seq(numtheory[tau](mul(ithprime(k), k=1..n)-1), n=1..30);
%t Map[DivisorSigma[0, #] &, -1 + FoldList[Times, Prime@ Range@ 30] ] (* _Michael De Vlieger_, Oct 25 2023 *)
%Y Cf. A057588, A000005, A054989, A366809, A064145.
%K nonn
%O 1,2
%A _Sean A. Irvine_, Oct 23 2023