A336612 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).

1, 3, 4, 12, 14, 21, 30, 35, 64, 77, 84, 91, 105, 119, 133, 135, 140, 144, 161, 162, 165, 192, 195, 203, 217, 224, 255, 259, 285, 287, 301, 308, 329, 336, 343, 345, 360, 364, 371, 375, 392, 413, 420, 427, 435, 465, 468, 469, 476, 480, 497, 511, 532, 540, 553, 555, 576

Offset: 1

Author

Bernard Schott, Jul 27 2020

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

Cf. A000005, A000203, A062069.

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

Programs

Maple

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

Mathematica

Select[Range[600], Divisible[#, DivisorSigma[1, DivisorSigma[0, #]]] &] (* Amiram Eldar, Jul 27 2020 *)

PARI

isok(m) = !(m % sigma(numdiv(m))); \\ Michel Marcus, Jul 29 2020