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A338172
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a(n) is the product of those divisors d of n such that tau(d) divides sigma(d).
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3
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1, 1, 3, 1, 5, 18, 7, 1, 3, 5, 11, 18, 13, 98, 225, 1, 17, 18, 19, 100, 441, 242, 23, 18, 5, 13, 81, 98, 29, 40500, 31, 1, 1089, 17, 1225, 18, 37, 722, 1521, 100, 41, 1555848, 43, 10648, 10125, 1058, 47, 18, 343, 5, 2601, 13, 53, 26244, 3025, 5488, 3249, 29
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OFFSET
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1,3
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COMMENTS
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a(n) is the product of arithmetic divisors d of n.
a(n) = pod(n) = A007955(n) for numbers n from A334420.
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LINKS
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Table of n, a(n) for n=1..58.
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FORMULA
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a(p) = p for odd primes p (A065091).
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EXAMPLE
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a(6) = 18 because there are 3 arithmetic divisors of 6 (1, 3 and 6): sigma(1)/tau(1) = 1/1 = 1; sigma(3)/tau(3) = 4/2 = 2; sigma(6)/tau(6) = 12/4 = 3. Product of this divisors is 18.
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MATHEMATICA
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a[n_] := Times @@ Select[Divisors[n], Divisible[DivisorSigma[1, #], DivisorSigma[0, #]] &]; Array[a, 100] (* Amiram Eldar, Oct 15 2020 *)
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PROG
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(MAGMA) [&*[d: d in Divisors(n) | IsIntegral(&+Divisors(d) / #Divisors(d))]: n in [1..100]]
(PARI) a(n) = my(d=divisors(n)); prod(k=1, #d, if (sigma(d[k]) % numdiv(d[k]), 1, d[k])); \\ Michel Marcus, Oct 15 2020
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CROSSREFS
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Cf. A000005 (tau), A000203 (sigma), A003601 (arithmetic numbers).
Cf. A334420, A334421.
See A338170 and A338171 for number and sum of such divisors.
Sequence in context: A181836 A124740 A347556 * A104053 A187369 A039512
Adjacent sequences: A338169 A338170 A338171 * A338173 A338174 A338175
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KEYWORD
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nonn
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AUTHOR
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Jaroslav Krizek, Oct 14 2020
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STATUS
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approved
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