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A053783 (1+e)-harmonic numbers: harmonic mean of (1+e)-divisors is integral. 2
1, 6, 28, 140, 728, 1638, 2184, 3640, 8008, 8190, 10920, 18620, 23808, 23895, 27846, 37128, 47790, 55860, 69160, 148960, 166656, 189810, 237510, 242060, 316680, 334530, 359600, 406215, 446880, 484120, 525690, 669060, 726180, 1029952, 1078800, 1089270, 1099170 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If n = Product p(i)^r(i), d = Product p(i)^s(i) and s(i) = 0 or s(i) divides r(i), then d is a (1+e)-divisor of n.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..100

MATHEMATICA

f[p_, e_] := (DivisorSigma[0, e] + 1)/(p^e + DivisorSum[e, p^(e - #) &]); aQ[n_] := IntegerQ[n * Times @@ (f @@@ FactorInteger[n])]; Select[Range[10^5], aQ] (* Amiram Eldar, Sep 07 2019 *)

CROSSREFS

Cf. A001599, A049599, A051378.

Sequence in context: A335316 A335317 A074247 * A216383 A283094 A110047

Adjacent sequences:  A053780 A053781 A053782 * A053784 A053785 A053786

KEYWORD

nonn

AUTHOR

Naohiro Nomoto, Apr 14 2001

EXTENSIONS

More terms from Amiram Eldar, Sep 07 2019

STATUS

approved

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Last modified August 11 13:02 EDT 2020. Contains 336428 sequences. (Running on oeis4.)