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.
%I A140688 #22 Feb 16 2025 08:33:08
%S A140688 12285,67095,71145,87633,142310
%N A140688 List of numbers which are both amicable and friendly.
%C A140688 There are almost certainly many other amicables both within and without the displayed range which also are friendly, but they have not yet been identified.
%C A140688 The usual OEIS policy is to display sequences only as far as they are known to be complete. How far is this sequence known to be complete? - _N. J. A. Sloane_, Jul 12 2008. The answer appears to be that nothing is known for certain. It may well be that 12285 is not even the first term! - _N. J. A. Sloane_, Dec 04 2008
%C A140688 It is not known if the two smallest amicable numbers, 220 and 284, are friendly. In fact it is not even known if 10 is friendly. - _Walter Nissen_, Dec 02 2008
%C A140688 The following numbers are all known to be members of this sequence: 12285, 67095, 71145, 87633, 142310, 525915, 863835, 947835, 1125765, 1798875, 3606850, 5357625, 5684679, 5730615, 6088905, 9206925, 9478910, 9491625, 10634085, 12361622, 13671735, 14426230, 17041010, 17257695, 17754165, 20308995, 20955645, 22227075, 22508145, 23111055, 23389695, 25132545, 34765731, 35115795, 36939357, 43266285, 53011395, 66595130, 74769345, 80422335, 82824255, 82977345, 84591405. - _Dean Hickerson_, Dec 02 2008 (communicated by _Walter Nissen_). However, until we have more definite information about the correctness of the first five terms (there could be additional terms less than 142310), there is no point in adding these terms to the "DATA" line. - _N. J. A. Sloane_, Nov 23 2011
%D A140688 Dean Hickerson, "Re: Friendly number", post to sci.math newsgroup, 2000, available through groups.google.com.
%D A140688 Ore, Oystein, Number Theory and Its History, McGraw-Hill, 1948, reprinted 1988, section 5-3, pp 96-100.
%H A140688 Claude W. Anderson and Dean Hickerson, <a href="https://www.jstor.org/stable/2318325">Problem 6020: Friendly Integers</a>, Amer. Math. Monthly 84 (1977) pp. 65-66.
%H A140688 Walter Nissen, <a href="http://upforthecount.com/math/abundance.html">Abundancy : Some Resources </a>
%H A140688 Walter Nissen, <a href="http://upforthecount.com/math/mandrill.html">Primitive Friendly Integers and Exclusive Multiples</a>
%H A140688 J. O. M. Pedersen, <a href="http://amicable.homepage.dk/knwnap.htm">Known Amicable Pairs</a> [Broken link]
%H A140688 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FriendlyPair.html">Friendly Pair</a>
%e A140688 (69615, 87633) are an amicable pair with sigma = 157248. { 14445, 87633 } are a friendly pair of abundancy = 192/107. Therefore 87633 is a member of the sequence.
%e A140688 The smallest friend of 3606850 is 7521154875.
%Y A140688 Cf. A063990, A074902.
%K A140688 more,nonn
%O A140688 1,1
%A A140688 _Walter Nissen_, Jul 11 2008
%E A140688 Edited by _N. J. A. Sloane_, Dec 04 2008 and Nov 23 2011