A260146 Number of positive divisors of hyperfactorial(n).

1, 1, 3, 12, 44, 264, 1020, 8160, 19680, 55104, 182784, 2193408, 4608000, 64512000, 210524160, 560849520, 964157040, 17354826720, 32092508448, 641850168960, 1302952210560, 3134374548480, 9806680558080, 235360333393920, 374108929689600, 740882390169600

Offset: 0

Author

Matthew Campbell, Jul 17 2015

Keywords

• nonn
• easy

Examples

			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.
		

Links

• Matthew Campbell and Charles R Greathouse IV, Table of n, a(n) for n = 0..1866 (terms 0..677 from Campbell)

Crossrefs

Cf. A000005, A002109.

Programs

Mathematica

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

PARI

hf(n,p)=my(s); forstep(k=p,n,p, s+=k); if(nhf(n,p)+1, primes([2,n]))) \\ Charles R Greathouse IV, Jul 17 2015

Formula

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