A336612 - OEIS

%I #14 Jul 29 2020 18:43:04

%S 1,3,4,12,14,21,30,35,64,77,84,91,105,119,133,135,140,144,161,162,165,

%T 192,195,203,217,224,255,259,285,287,301,308,329,336,343,345,360,364,

%U 371,375,392,413,420,427,435,465,468,469,476,480,497,511,532,540,553,555,576

%N Numbers m such that sigma(tau(m)) divides m, where tau(m) is the number of divisors function (A000005) and sigma(m) is the sum of divisors function (A000203).

%C Every 7*p with p prime <> 7 is a term because 7*p / sigma(tau(7*p)) = p (see example).

%e 35 = 7 * 5, tau(35) = 4, sigma(tau(35)) = sigma(4) = 4 + 2 + 1 = 7 and 35/7 = 5 hence 35 is a term.

%p with(numtheory) filter:= m -> m/sigma(tau(m)) = floor(m/sigma(tau(m))) : select(filter, [$1..600]);

%t Select[Range[600], Divisible[#, DivisorSigma[1, DivisorSigma[0, #]]] &] (* _Amiram Eldar_, Jul 27 2020 *)

%o (PARI) isok(m) = !(m % sigma(numdiv(m))); \\ _Michel Marcus_, Jul 29 2020

%Y Cf. A000005, A000203, A062069.

%Y Cf. A336613 (tau(sigma(m)) divides m).

%K nonn

%O 1,2

%A _Bernard Schott_, Jul 27 2020