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A338395
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Numbers m such that lcm(tau(m), sigma(m), pod(m)) = pod(m).
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2
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1, 6, 30, 66, 84, 102, 120, 210, 270, 318, 330, 420, 462, 510, 546, 570, 642, 672, 690, 714, 840, 870, 924, 930, 966, 1080, 1092, 1122, 1320, 1410, 1428, 1518, 1590, 1638, 1722, 1770, 1890, 1932, 2040, 2130, 2226, 2280, 2310, 2346, 2370, 2604, 2670, 2730, 2760
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OFFSET
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1,2
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COMMENTS
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Numbers m such that both values tau(m) and sigma(m) divide pod(m).
Numbers m such that all values m, tau(m) and sigma(m) divide pod(m); i.e. lcm(m, tau(m), sigma(m), pod(m)) = pod(m).
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LINKS
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EXAMPLE
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lcm(tau(6), sigma(6), pod(6)) = lcm(4, 12, 36) = 36 = pod(6).
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MATHEMATICA
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Select[Range[3000], LCM @@ {(d = DivisorSigma[0, #]), DivisorSigma[1, #], (pod = #^(d/2))} == pod &] (* Amiram Eldar, Oct 24 2020 *)
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PROG
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(Magma) [m: m in [1..10^5] | LCM([#Divisors(m), &+Divisors(m), &*Divisors(m)]) eq &*Divisors(m)]
(PARI) isok(m) = my(d=divisors(m), prd=vecprod(d)); lcm([#d, vecsum(d), prd]) == prd; \\ Michel Marcus, Oct 24 2020
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CROSSREFS
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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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