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

0,3

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(PARI) hf(n, p)=my(s); forstep(k=p, n, p, s+=k); if(n<p^2, s, p*hf(n\p, p)+s)
a(n)=factorback(apply(p->hf(n, p)+1, primes([2, n]))) \\ Charles R Greathouse IV, Jul 17 2015

Crossrefs

Cf. A000005, A002109.

Sequence in context: A331473 A005656 A339066 * A229936 A258626 A064017

Adjacent sequences: A260143 A260144 A260145 * A260147 A260148 A260149

Keyword

nonn,easy

Author

Matthew Campbell, Jul 17 2015

Status

approved