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.

A349027 Exponential unitary harmonic numbers (A349026) that are not squarefree.

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%I A349027 #9 Nov 06 2021 12:04:49
%S A349027 12,18,36,40,60,75,84,90,120,126,132,135,144,150,156,180,198,204,228,
%T A349027 234,252,270,276,280,306,342,348,360,372,396,414,420,440,444,450,468,
%U A349027 492,516,520,522,525,540,544,558,564,588,600,612,630,636,660,666,675,680
%N A349027 Exponential unitary harmonic numbers (A349026) that are not squarefree.
%C A349027 First differs from A348965 at n = 13.
%C A349027 All squarefree numbers are exponential unitary harmonic numbers.
%H A349027 Amiram Eldar, <a href="/A349027/b349027.txt">Table of n, a(n) for n = 1..10000</a>
%H A349027 Nicuşor Minculete, <a href="http://www.imar.ro/~purice/Inst/2012/Minculete-Dr.pdf">Contribuţii la studiul proprietăţilor analitice ale funcţiilor aritmetice - Utilizarea e-divizorilor</a>, Ph.D. thesis, Academia Română, 2012. See section 4.3, pp. 90-94.
%e A349027 12 = 2^2 * 3 is a term since it is not squarefree, its exponential unitary divisors are 6 and 12, and their harmonic mean, 8, is an integer.
%t A349027 f[p_, e_] := p^e * 2^PrimeNu[e] / DivisorSum[e, p^(e - #) &, CoprimeQ[#, e/#] &]; euhQ[1] = True; euhQ[n_] := IntegerQ[Times @@ f @@@ FactorInteger[n]]; Select[Range[1000], ! SquareFreeQ[#] && euhQ[#] &]
%Y A349027 Intersection of A013929 and A349026.
%Y A349027 Cf. A005117, A348965.
%K A349027 nonn
%O A349027 1,1
%A A349027 _Amiram Eldar_, Nov 06 2021