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.

A307098 The primitive abundant numbers k (A071395) arranged by the decreasing values of their abundancy index sigma(k)/k.

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%I A307098 #30 May 12 2019 22:22:14
%S A307098 3465,15015,4095,1430,19635,16796,20,21945,5355,692835,2584,5985,
%T A307098 23205,49742,20332,22309287,26565,188955,1870,216315,838695,25935,
%U A307098 3128,22724,6084351,7245,2090,60214,2107575,937365,1542773001,25636,28129101,33495,13066965,3016174
%N A307098 The primitive abundant numbers k (A071395) arranged by the decreasing values of their abundancy index sigma(k)/k.
%C A307098 Cohen proved that for any given eps > 0 there are only finitely many primitive abundant numbers k with sigma(k)/k >= 2 + eps. Thus the primitive abundant numbers can be arranged by their decreasing value of their abundancy index. In case of more than one primitive abundant number with the same abundancy index, the terms are ordered by their value.
%C A307098 Cohen calculated the first 91 terms of this sequence, all the terms with abundancy index >= 2.05 - see the link for the corresponding values of the abundancy index.
%H A307098 Amiram Eldar, <a href="/A307098/b307098.txt">Table of n, a(n) for n = 1..91</a>
%H A307098 Graeme L. Cohen, <a href="https://doi.org/10.1017/S1446788700019819">On primitive abundant numbers</a>, Journal of the Australian Mathematical Society, Vol. 34 No. 1 (1983), pp. 123-137.
%H A307098 Amiram Eldar, <a href="/A307098/a307098.txt">Table of n, a(n), prime factorization of a(n), sigma(a(n))/a(n) (rounded) for n = 1..91</a>
%e A307098 a(1) = 3465 since it is the primitive abundant number (A071395) with the largest possible abundancy index among the primitive abundant numbers: sigma(3465)/3465 = 832/385 = 2.161003...
%Y A307098 Cf. A000203, A005100, A005101, A071395.
%K A307098 nonn
%O A307098 1,1
%A A307098 _Amiram Eldar_, Mar 25 2019