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A020696
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Let a,b,c,...k be all divisors of n; a(n) = (a+1)*(b+1)*...*(k+1).
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11
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2, 6, 8, 30, 12, 168, 16, 270, 80, 396, 24, 10920, 28, 720, 768, 4590, 36, 31920, 40, 41580, 1408, 1656, 48, 2457000, 312, 2268, 2240, 104400, 60, 5499648, 64, 151470, 3264, 3780, 3456, 76767600, 76, 4680, 4480, 15343020, 84, 19071360, 88, 372600, 353280, 6768
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OFFSET
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1,1
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COMMENTS
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Named "Vandiver's arithmetical function" by Sándor (2021), after the American mathematician Harry Schultz Vandiver (1882-1973). - Amiram Eldar, Jun 29 2022
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LINKS
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Harry S. Vandiver, Problem 116, American Mathematical Monthly, Vol. 11, No. 2 (1904), pp. 38-39.
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FORMULA
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a(p) = 2(p+1), a(p^2) = 2(p+1)(p^2+1) for primes p.
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MAPLE
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a:= n-> mul(d+1, d=numtheory[divisors](n)):
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MATHEMATICA
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Table[Times @@ (Divisors[n] + 1), {n, 43}] (* Ivan Neretin, May 27 2015 *)
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PROG
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(PARI) a(n) = {d = divisors(n); return (prod(i=1, #d, d[i]+1)); } \\ Michel Marcus, Jun 12 2013
(Haskell)
a020696 = product . map (+ 1) . a027750_row'
(Python)
from math import prod
from sympy import divisors
def A020696(n): return prod(d+1 for d in divisors(n, generator=True)) # Chai Wah Wu, Jun 30 2022
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CROSSREFS
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Cf. A057643 (LCM instead of product).
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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