cp's OEIS Frontend

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).

%I A336687 #24 Aug 06 2020 05:05:55
%S A336687 1,3,4,12,64,84,140,144,162,192,336,360,420,468,480,576,600,644,720,
%T A336687 780,1008,1344,1512,1584,1600,1740,1872,2160,2240,2448,2592,2736,2880,
%U A336687 2884,3136,3240,3888,4032,4158,4228,4464,4608,4800,5040,5115,5184,5328,5670,6060,6192,6336
%N 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).
%C A336687 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 A336687 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 A336687 with(numtheory):
%p A336687 filter:= m-> irem(m, tau(sigma(m)))=0 and irem(m, sigma(tau(m)))=0:
%p A336687 select(filter, [$1..7000])[];
%t A336687 Select[Range[6400], And @@ Divisible[#, {DivisorSigma[0, DivisorSigma[1, #]], DivisorSigma[1, DivisorSigma[0, #]]}] &] (* _Amiram Eldar_, Jul 31 2020 *)
%o A336687 (PARI) isok(m) = !(m % numdiv(sigma(m))) && !(m % sigma(numdiv(m))); \\ _Michel Marcus_, Aug 02 2020
%Y A336687 Cf. A000005, A000203, A062068, A062069.
%Y A336687 Intersection of A336612 and A336613.
%K A336687 nonn
%O A336687 1,2
%A A336687 _Bernard Schott_, Jul 31 2020