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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.

A349019 Modified e-perfect numbers: numbers k such that A348963(k) | k.

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%I A349019 #14 Aug 06 2024 06:08:49
%S A349019 1,2,3,5,6,7,10,11,12,13,14,15,17,19,21,22,23,26,29,30,31,33,34,35,36,
%T A349019 37,38,39,40,41,42,43,46,47,51,53,55,57,58,59,60,61,62,65,66,67,69,70,
%U A349019 71,73,74,77,78,79,82,83,84,85,86,87,89,91,93,94,95,97,101
%N A349019 Modified e-perfect numbers: numbers k such that A348963(k) | k.
%C A349019 First differs from A225354 at n = 25.
%C A349019 Not to be confused with modified exponential perfect numbers (A323757).
%C A349019 Sándor (2006) showed that the exponential harmonic numbers of type 2 (A348964) are terms in this sequence.
%C A349019 All the squarefree numbers are terms (A005117), since A348963(k) = 1 if k is squarefree.
%H A349019 Amiram Eldar, <a href="/A349019/b349019.txt">Table of n, a(n) for n = 1..10000</a>
%H A349019 József Sándor, <a href="https://citeseerx.ist.psu.edu/pdf/2936ca1cfcb9e3673ed4165dca32dbee1f4070f5">On exponentially harmonic numbers</a>, Scientia Magna, Vol. 2, No. 3 (2006), pp. 44-47.
%H A349019 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 A349019 12 is a term since A348963(12) = 3 is a divisor of 12.
%t A349019 f[p_, e_] := p^e/DivisorSum[e, p^(e - #) &]; modEPerfQ[1] = True; modEPerfQ[n_] := IntegerQ[Times @@ f @@@ FactorInteger[n]]; Select[Range[100], modEPerfQ]
%Y A349019 A005117, A348964 and A349020 are subsequences.
%Y A349019 Cf. A225354, A323757, A348963.
%K A349019 nonn
%O A349019 1,2
%A A349019 _Amiram Eldar_, Nov 06 2021