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A336723
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a(n) = lcm(tau(n), sigma(n), pod(n)) where tau(k) is the number of divisors of k (A000005), sigma(k) is the sum of divisors of k (A000203) and pod(k) is the product of divisors of k (A007955).
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6
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1, 6, 12, 168, 30, 36, 56, 960, 351, 900, 132, 12096, 182, 1176, 1800, 158720, 306, 75816, 380, 168000, 14112, 4356, 552, 1658880, 11625, 14196, 29160, 65856, 870, 810000, 992, 2064384, 17424, 31212, 58800, 917070336, 1406, 21660, 85176, 23040000, 1722, 6223392
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OFFSET
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1,2
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COMMENTS
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a(n) = pod(n) for numbers n: 1, 6, 30, 66, 84, 102, 120, 210, 270, 318, 330, 420, 462, 510, 546, 570, 642, ...
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LINKS
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FORMULA
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a(p) = p^2 + p for p = primes (A000040).
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EXAMPLE
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a(6) = lcm(tau(6), sigma(6), pod(6)) = lcm(4, 12, 36) = 36.
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MATHEMATICA
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a[n_] := LCM @@ {(d = DivisorSigma[0, n]), DivisorSigma[1, n], n^(d/2)}; Array[a, 50] (* Amiram Eldar, Aug 01 2020 *)
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PROG
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(Magma) [LCM([#Divisors(n), &+Divisors(n), &*Divisors(n)]): n in [1..100]]
(PARI) a(n) = my(d=divisors(n)); lcm([#d, vecsum(d), vecprod(d)]); \\ Michel Marcus, Aug 12 2020
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CROSSREFS
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Cf. A277521 (numbers k such that a(k) = pod(k) and simultaneously A336722(k) = tau(k)).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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