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%I #24 Aug 06 2020 05:05:55
%S 1,3,4,12,64,84,140,144,162,192,336,360,420,468,480,576,600,644,720,
%T 780,1008,1344,1512,1584,1600,1740,1872,2160,2240,2448,2592,2736,2880,
%U 2884,3136,3240,3888,4032,4158,4228,4464,4608,4800,5040,5115,5184,5328,5670,6060,6192,6336
%N 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).
%C 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
%e 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.
%p with(numtheory):
%p filter:= m-> irem(m, tau(sigma(m)))=0 and irem(m, sigma(tau(m)))=0:
%p select(filter, [$1..7000])[];
%t Select[Range[6400], And @@ Divisible[#, {DivisorSigma[0, DivisorSigma[1, #]], DivisorSigma[1, DivisorSigma[0, #]]}] &] (* _Amiram Eldar_, Jul 31 2020 *)
%o (PARI) isok(m) = !(m % numdiv(sigma(m))) && !(m % sigma(numdiv(m))); \\ _Michel Marcus_, Aug 02 2020
%Y Cf. A000005, A000203, A062068, A062069.
%Y Intersection of A336612 and A336613.
%K nonn
%O 1,2
%A _Bernard Schott_, Jul 31 2020
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