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

Author

Naohiro Nomoto, Apr 14 2001

Keywords

• nonn

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

Crossrefs

Cf. A001599, A049599, A051378, A053784.

Programs

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 *)

Extensions

More terms from Amiram Eldar, Sep 07 2019