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A336687 Numbers m such that tau(sigma(m)) and sigma(tau(m)) both divide m, where tau(m) is the number of divisors function (A000005) and sigma(m) is the sum of divisors function (A000203). 0
1, 3, 4, 12, 64, 84, 140, 144, 162, 192, 336, 360, 420, 468, 480, 576, 600, 644, 720, 780, 1008, 1344, 1512, 1584, 1600, 1740, 1872, 2160, 2240, 2448, 2592, 2736, 2880, 2884, 3136, 3240, 3888, 4032, 4158, 4228, 4464, 4608, 4800, 5040, 5115, 5184, 5328, 5670, 6060, 6192, 6336 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Conjecture: The only m such that m = tau(sigma(m))*sigma(tau(m)) are in {1,468,3240}. Verified for m up to 1*10^9. - Ivan N. Ianakiev, Aug 06 2020
LINKS
EXAMPLE
For 84: tau(84) = 12 and sigma(12) = 28 with 84/28 = 3. Also, sigma(84) = 224 and tau(224) = 12 with 84/12 = 7. Hence, 84 is a term.
MAPLE
with(numtheory):
filter:= m-> irem(m, tau(sigma(m)))=0 and irem(m, sigma(tau(m)))=0:
select(filter, [$1..7000])[];
MATHEMATICA
Select[Range[6400], And @@ Divisible[#, {DivisorSigma[0, DivisorSigma[1, #]], DivisorSigma[1, DivisorSigma[0, #]]}] &] (* Amiram Eldar, Jul 31 2020 *)
PROG
(PARI) isok(m) = !(m % numdiv(sigma(m))) && !(m % sigma(numdiv(m))); \\ Michel Marcus, Aug 02 2020
CROSSREFS
Intersection of A336612 and A336613.
Sequence in context: A299809 A109771 A052626 * A298115 A122903 A059792
KEYWORD
nonn
AUTHOR
Bernard Schott, Jul 31 2020
STATUS
approved

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Last modified June 14 04:14 EDT 2024. Contains 373393 sequences. (Running on oeis4.)