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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).
2
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).
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. A336613 (tau(sigma(m)) divides m).
Sequence in context: A324653 A094025 A376979 * A070287 A124637 A352907
KEYWORD
nonn
AUTHOR
Bernard Schott, Jul 27 2020
STATUS
approved