A053784 Harmonic means of (1+e)-divisors of (1+e)-harmonic numbers.

1, 2, 3, 5, 6, 9, 9, 10, 11, 15, 15, 14, 8, 9, 17, 17, 12, 21, 19, 16, 14, 18, 29, 26, 29, 21, 20, 17, 24, 28, 22, 27, 39, 24, 30, 42, 23, 42, 48, 33, 26, 54, 41, 35, 37, 36, 34, 39, 31, 44, 40, 36, 38, 46, 51, 55, 77, 41, 60, 77, 54, 57, 88, 47, 43, 45, 46, 99

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 - #) &]); h[n_] := n*Times @@ (f @@@ FactorInteger[n]); Select[h /@ Range[10^5], IntegerQ] (* Amiram Eldar, Sep 07 2019*)

Crossrefs

Cf. A049599, A051378, A053783.

Sequence in context: A118809 A121048 A075389 * A036697 A131292 A276476

Adjacent sequences: A053781 A053782 A053783 * A053785 A053786 A053787

Keyword

nonn

Author

Naohiro Nomoto, Apr 14 2001

Extensions

More terms from Amiram Eldar, Sep 07 2019

Status

approved