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A260146 Number of positive divisors of hyperfactorial(n). 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 17 20:44 EDT 2021. Contains 343990 sequences. (Running on oeis4.)