A053783 (1+e)-harmonic numbers: harmonic mean of (1+e)-divisors is an integer.

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

Offset

1,2

Comments

If k = 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 k.

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, A053784.

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