

A335387


Triunitary harmonic numbers: numbers k such that the harmonic mean of the triunitary divisors of k is an integer.


2



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
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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 triunitary 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 (biunitary), A319745 (nonunitary).
Cf. A324706, A335385.
Sequence in context: A077672 A119202 A286325 * A063947 A006086 A273507
Adjacent sequences: A335384 A335385 A335386 * A335388 A335389 A335390


KEYWORD

nonn


AUTHOR

Amiram Eldar, Jun 04 2020


STATUS

approved



