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A336745 Numbers m that divide the product phi(m) * sigma(m) * tau(m), where phi is the Euler totient function (A000010), sigma is the sum of divisors function (A000203) and tau is the number of divisors function (A000005). 3
1, 2, 6, 8, 9, 12, 18, 24, 28, 32, 36, 40, 54, 72, 80, 84, 96, 108, 117, 120, 128, 135, 144, 162, 196, 200, 216, 224, 234, 240, 243, 252, 270, 288, 324, 360, 384, 400, 405, 448, 468, 486, 496, 512, 540, 576, 588, 600, 625, 640, 648, 672, 675, 720, 756, 768, 775, 810, 819 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If s and t are terms with gcd(s, t) = 1, then s*t is another term as phi, sigma and tau are multiplicative functions.

The only prime term is 2 because prime p must divide 2*(p-1)*(p+1) to be a term.

LINKS

David A. Corneth, Table of n, a(n) for n = 1..10000

EXAMPLE

For 24, phi(24) = 8, sigma(24) = 60 and tau(24) = 8, then 8*60*8 / 24 = 160, hence 24 is a term.

MAPLE

with(numtheory):

filter:= m -> irem(tau(m)*phi(m)*sigma(m), m) =0:

select(filter, [$1..850]);

MATHEMATICA

Select[Range[1000], Divisible[Times @@ DivisorSigma[{0, 1}, #] * EulerPhi[#], #] &] (* Amiram Eldar, Aug 02 2020 *)

PROG

(PARI) isok(m) = !(eulerphi(m)*sigma(m)*numdiv(m) % m); \\ Michel Marcus, Aug 05 2020

CROSSREFS

Cf. A000005, A000010, A000203, A062355.

Subsequences: A000396 (perfect numbers), A005820 (tri-perfect), A027687 (4-perfect), A046060 (5-multiperfect), A046061 (6-multiperfect), A007691 (multiply-perfect numbers), A336715 (m divides phi(m)*tau(m)), A004171, A005010.

Sequence in context: A288428 A050675 A262981 * A034591 A047278 A242204

Adjacent sequences:  A336742 A336743 A336744 * A336746 A336747 A336748

KEYWORD

nonn

AUTHOR

Bernard Schott, Aug 02 2020

STATUS

approved

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Last modified August 15 02:47 EDT 2022. Contains 356122 sequences. (Running on oeis4.)