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 A280583 a(n) = product of divisors of the number of divisors of n. 1
 1, 2, 2, 3, 2, 8, 2, 8, 3, 8, 2, 36, 2, 8, 8, 5, 2, 36, 2, 36, 8, 8, 2, 64, 3, 8, 8, 36, 2, 64, 2, 36, 8, 8, 8, 27, 2, 8, 8, 64, 2, 64, 2, 36, 36, 8, 2, 100, 3, 36, 8, 36, 2, 64, 8, 64, 8, 8, 2, 1728, 2, 8, 36, 7, 8, 64, 2, 36, 8, 64, 2, 1728, 2, 8, 36, 36, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A007955(A000005(n)). a(p) = 2 for p = primes (A000040). a(n) = 3 for squares of primes (A001248). EXAMPLE For n = 6; a(n) = product of divisors (tau(6)) = 1*2*4 = 8. MATHEMATICA Table[Times@@Divisors[DivisorSigma[0, n]], {n, 80}] (* Harvey P. Dale, Dec 04 2021 *) PROG (Magma) [&*[d: d in Divisors(#[d: d in Divisors(n)])]: n in [1..100]] (Python) from math import isqrt from sympy import divisor_count def A280583(n): return (lambda m:(isqrt(m) if (c:=divisor_count(m)) & 1 else 1)*m**(c//2))(divisor_count(n)) # Chai Wah Wu, Jun 25 2022 CROSSREFS Cf. A000005, A000040, A001248, A007955, A010553, A062069. Sequence in context: A345281 A338319 A369748 * A177047 A339665 A334490 Adjacent sequences: A280580 A280581 A280582 * A280584 A280585 A280586 KEYWORD nonn AUTHOR Jaroslav Krizek, Jan 07 2017 STATUS approved

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Last modified June 12 10:35 EDT 2024. Contains 373331 sequences. (Running on oeis4.)