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 A175907 #22 Feb 16 2025 08:33:12
%S A175907 6,30,42,66,78,102,114,138,174,186,210,222,246,258,273,282,318,330,
%T A175907 354,366,390,402,426,438,462,474,498,510,534,546,570,582,606,618,642,
%U A175907 654,678,690,714,762,786,798,806,822,834,858,870,894,906,930,942,966,978,1002,1038
%N A175907 Known friendly squarefree numbers.
%C A175907 From _Walter Nissen_, May 28 2011: (Start)
%C A175907 As with most aspects of friendly and solitary numbers, this sequence is not known to be complete. A friend could possibly be found for 10, for example; same doubtful status as an odd perfect number.
%C A175907 Note that not all friendly numbers will be found among the primitive friendly numbers listed in link "Primitive Friendly Pairs", and this would be true even if those were not limited to small examples.
%C A175907 Other terms are 1330, 1995, and 49166.
%C A175907 (End)
%D A175907 Oystein Ore, Number Theory and Its History, McGraw-Hill, 1948, reprinted 1988, section 5-3, pp. 96-100.
%H A175907 Claude W. Anderson and Dean Hickerson, <a href="http://www.jstor.org/stable/2318325">Problem 6020: Friendly Integers</a>, Amer. Math. Monthly 84 (1977) pp. 65-66.
%H A175907 Richard Laatsch, <a href="http://www.jstor.org/stable/2690424">Measuring the abundancy of integers</a>, Mathematics Magazine 59 (2) (1986) 84-92.
%H A175907 Walter Nissen, <a href="http://upforthecount.com/math/ffp8.html">Primitive Friendly Pairs</a>
%H A175907 Walter Nissen, <a href="http://upforthecount.com/math/abundance.html">Abundancy: some resources</a>
%H A175907 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SolitaryNumber.html">Solitary Number</a>
%e A175907 6, being 2 * 3, is squarefree. Having abundancy = 2, 6 is friendly with all the other perfect numbers. Ergo, it is in the sequence. ( 1 ), 2, 3, and 5, being prime powers, are solitary. 4 is a square. Ergo, a(1) is 6.
%o A175907 (PARI) { for (j=1,2000, if (issquarefree(j), t=sigma(j)/j; for (i=1,1000000, p=sigma(i)/i; if(p == t && j != i, print(j," ",i); ); ); ); ); quit; } \\ provides useful suggestions, but not definitive, _Walter Nissen_, May 28 2011
%Y A175907 Cf. A005117, A014567, A074902 (known friendly numbers), A095751, A096366, A140688.
%K A175907 nonn
%O A175907 1,1
%A A175907 _Thomas Kellar_, Oct 14 2010, Oct 15 2010
%E A175907 Added 273 as it is friendly with 2876211; 273 is a counterexample to the conjecture that 6 divides a(n). - _Walter Nissen_, May 28 2011
%E A175907 Added 806 as it is friendly with 2449562488893. - _Suyash Pandit_, Jan 24 2024