A348965 - OEIS

%I #13 Aug 06 2024 06:06:57

%S 12,18,36,40,60,75,84,90,120,126,132,135,150,156,180,198,204,208,228,

%T 234,252,270,276,280,306,342,348,360,372,396,414,420,440,444,450,468,

%U 492,516,520,522,525,540,544,558,564,588,600,612,624,630,636,660,666,675

%N Exponential harmonic numbers of type 2 that are not squarefree.

%C Sándor (2006) proved that all squarefree numbers are exponential harmonic numbers of type 2.

%H Amiram Eldar, <a href="/A348965/b348965.txt">Table of n, a(n) for n = 1..10000</a>

%H József Sándor, <a href="http://citeseerx.ist.psu.edu/pdf/2936ca1cfcb9e3673ed4165dca32dbee1f4070f5">On exponentially harmonic numbers</a>, Scientia Magna, Vol. 2, No. 3 (2006), pp. 44-47.

%H József Sándor, <a href="https://blngcc.files.wordpress.com/2008/11/jozsel-sandor-selected-chaters-of-geometry-analysis-and-number-theory.pdf">Selected Chapters of Geomety, Analysis and Number Theory</a>, 2005, pp. 141-145.

%e 12 = 2^2 * 3 is a term since it is not squarefree, its exponential divisors are 6 and 12, and their harmonic mean, 8, is an integer.

%t f[p_, e_] := p^e * DivisorSigma[0, e] / DivisorSum[e, p^(e-#) &]; ehQ[1] = True; ehQ[n_] := IntegerQ[Times @@ f @@@ FactorInteger[n]]; Select[Range[1000], ! SquareFreeQ[#] && ehQ[#] &]

%Y Intersection of A013929 and A348964.

%Y Cf. A005117, A348962.

%K nonn

%O 1,1

%A _Amiram Eldar_, Nov 05 2021