A153789 First differences of harmonic (or Ore) numbers A001599.

5, 22, 112, 130, 226, 176, 966, 1332, 3230, 1928, 62, 10410, 20, 9226, 2394, 2520, 23100, 49804, 12136, 49600, 6200, 63910, 4550, 90580, 27720, 179040, 156120, 30660, 27300, 197496, 138294, 332010, 118440, 638820, 50960, 60760, 166740

Offset: 1

Author

Omar E. Pol, Jan 20 2009

Keywords

• nonn

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..71

Crossrefs

Cf. A001599.

Programs

GAP

H:=Concatenation([1],Filtered([2,4..3*10^6],n->IsInt(n*Tau(n)/Sigma(n))));;
a:=List([1..Length(H)-1],i->H[i+1]-H[i]);; Print(a); # Muniru A Asiru, Dec 23 2018

Mathematica

a := Select[Range[1000000], IntegerQ[HarmonicMean[Divisors[#]]] &]; Table[Part[a,n + 1] - Part[a,n], {n,1,30}] (* G. C. Greubel, Aug 29 2016 *)

Python

from numpy import diff
from sympy import divisor_sigma as sigma
def ore(n): return (n*sigma(n, 0))%sigma(n, 1) == 0
print(diff(list(filter(ore, range(1, 9000))))) # Michael S. Branicky, May 22 2021

Extensions

More terms from R. J. Mathar, Feb 19 2009