A335387 Tri-unitary harmonic numbers: numbers k such that the harmonic mean of the tri-unitary divisors of k is an integer.

1, 6, 45, 60, 90, 270, 420, 630, 2970, 5460, 8190, 9100, 15925, 27300, 36720, 40950, 46494, 47520, 54600, 81900, 95550, 136500, 163800, 172900, 204750, 232470, 245700, 257040, 332640, 409500, 464940, 491400, 646425, 716625, 790398, 791700, 819000, 900900, 929880

Offset

1,2

Comments

Equivalently, numbers k such that A324706(k) | (k * A335385(k)).

Differs from A063947 from n >= 18.

Links

Amiram Eldar, Table of n, a(n) for n = 1..200

Example

45 is a term since its tri-unitary divisors are {1, 5, 9, 45} and their harmonic mean, 3, in an integer.

Mathematica

f1[p_, e_] := If[e == 3 || e == 6, 4, 2]; f2[p_, e_] := If[e == 3, (p^4 - 1)/(p - 1), If[e == 6, (p^8 - 1)/(p^2 - 1), p^e + 1]]; f[p_, e_] := p^e * f1[p, e]/f2[p, e]; tuhQ[1] = True; tuhQ[n_] := IntegerQ[Times @@ (f @@@ FactorInteger[n])]; Select[Range[10^4], tuhQ]

Crossrefs

A324707 is a subsequence.

Analogous sequences: A001599 (harmonic numbers), A006086 (unitary), A063947 (infinitary), A286325 (bi-unitary), A319745 (nonunitary).

Cf. A324706, A335385.

Sequence in context: A119202 A367561 A286325 * A063947 A006086 A273507

Adjacent sequences: A335384 A335385 A335386 * A335388 A335389 A335390

Keyword

nonn

Author

Amiram Eldar, Jun 04 2020

Status

approved