cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A353038 Unitary harmonic numbers (A006086) that are not unitary arithmetic numbers (A103826).

This page as a plain text file.
%I A353038 #7 Apr 19 2022 07:26:37
%S A353038 90,40682250,81364500,105773850,423095400,1798155450,14385243600
%N A353038 Unitary harmonic numbers (A006086) that are not unitary arithmetic numbers (A103826).
%C A353038 There are 290 unitary harmonic numbers below 10^12, and only 7 of them are in this sequence.
%e A353038 90 is in the sequence since its unitary divisors are {1, 2, 5, 9, 10, 18, 45, 90}, their harmonic mean, 4, is an integer, but their arithmetic mean, 45/2, is not.
%t A353038 q[n_] := Module[{f = FactorInteger[n], d, s}, d = 2^Length[f]; s = Times @@ (1 + Power @@@ f); IntegerQ[n*d/s] && !IntegerQ[s/d]]; Select[Range[5*10^7], q]
%Y A353038 The unitary version of A046999.
%Y A353038 Subsequence of A006086.
%Y A353038 Cf. A006087, A103826.
%K A353038 nonn,more
%O A353038 1,1
%A A353038 _Amiram Eldar_, Apr 19 2022