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

1,2

Comments

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

Links

Table of n, a(n) for n=1..57.

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000005, A000203, A062069.

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

Sequence in context: A332206 A324653 A094025 * A070287 A124637 A352907

Adjacent sequences: A336609 A336610 A336611 * A336613 A336614 A336615

Keyword

nonn

Author

Bernard Schott, Jul 27 2020

Status

approved