A141551 Numbers k with property that if d divides k, then tau(tau(d)) also divides k.

1, 2, 4, 6, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 180, 192, 204, 228, 240, 252, 276, 288, 300, 324, 348, 360, 372, 396, 444, 468, 480, 492, 516, 564, 576, 588, 600, 612, 636, 684, 708, 720, 732, 804, 828, 840, 852, 876, 900, 948, 960, 972, 996, 1044, 1068

Offset: 1

Author

N. J. A. Sloane, Sep 12 2008

Keywords

• nonn

Comments

tau() = A000005().

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A010553, A141586.

Programs

Maple

with(numtheory); isA141551 := proc(n) local dvs,d; dvs := divisors(n) ; for d in dvs do if not tau(tau(d)) in dvs then RETURN(false): fi; od: RETURN(true); end:
t1:=[]; for n from 1 to 60000 do if isA141551(n) then t1:=[op(t1),n]; fi; od:

Mathematica

aQ[n_] := AllTrue[Divisors[n], Divisible[n, DivisorSigma[0, DivisorSigma[0, #]]] &]; Select[Range[1000], aQ] (* Amiram Eldar, Jul 08 2019 *)