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Number of positive divisors of hyperfactorial(n).
3

%I #26 Jun 03 2018 02:04:55

%S 1,1,3,12,44,264,1020,8160,19680,55104,182784,2193408,4608000,

%T 64512000,210524160,560849520,964157040,17354826720,32092508448,

%U 641850168960,1302952210560,3134374548480,9806680558080,235360333393920,374108929689600,740882390169600

%N Number of positive divisors of hyperfactorial(n).

%H Matthew Campbell and Charles R Greathouse IV, <a href="/A260146/b260146.txt">Table of n, a(n) for n = 0..1866</a> (terms 0..677 from Campbell)

%F a(n) = A000005(A002109(n)).

%e a(2) = sigma(0, hyperfactorial(2)) = sigma(0, 2^2*1^1) = sigma(0, 4). The divisors of 4 are 1, 2, and 4. The number of divisors is a(2) = 3.

%t Table[DivisorSigma[0, Hyperfactorial[n]], {n, 0, 200}]

%o (PARI) hf(n,p)=my(s); forstep(k=p,n,p, s+=k); if(n<p^2, s, p*hf(n\p,p)+s)

%o a(n)=factorback(apply(p->hf(n,p)+1, primes([2,n]))) \\ _Charles R Greathouse IV_, Jul 17 2015

%Y Cf. A000005, A002109.

%K nonn,easy

%O 0,3

%A _Matthew Campbell_, Jul 17 2015