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 A074902 #29 Apr 15 2025 12:53:27 %S A074902 6,12,24,28,30,40,42,56,60,66,78,80,84,96,102,108,114,120,132,135,138, %T A074902 140,150,168,174,186,200,204,210,222,224,228,234,240,246,252,258,264, %U A074902 270,273,276,280,282,294,300,308,312,318,330,348,354,360,364,366,372 %N A074902 Known friendly numbers. %C A074902 The sequence is not known to be complete up to 372, since there are many small numbers, including 10, 14, 15 and 20, which have not been proved to be solitary. If any other numbers up to 372 are friendly, the smallest corresponding values of m are > 10^30. %C A074902 A positive integer n is 'friendly' if abundancy(n) = abundancy(m) for some positive integer m not equal to n, where abundancy(n) = sigma(n)/n (cf. A000203); otherwise n is 'solitary'. (The name "friendly" is also sometimes mistakenly used with other meanings; cf. A063990 and A007770.) %C A074902 All perfect numbers are friendly numbers, but they are only friendly with each other (a perfect number being defined as having abundancy index of 2.) - _Daniel Forgues_, Jun 23 2009 %C A074902 Triangle A211679 has rows that list the first numbers that have n-1 smaller friends. Sequence A211677 lists just the last number in each row. - _T. D. Noe_, May 10 2012 %H A074902 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 A074902 Sagar Mandal, <a href="https://arxiv.org/abs/2412.02701">Prime Divisors of 10's Friends: A Generalization of Prior Bounds</a>, arXiv:2412.02701 [math.GM], 2024. See p. 10. %H A074902 Sagar Mandal, <a href="https://doi.org/10.13140/RG.2.2.14247.05283">Exploring the relationships between the divisors of friends of 10</a>, Bull. Calcutta Math. Soc. (2025) Vol. 48, No. 1-3, 21-32. %H A074902 Sagar Mandal and Sourav Mandal, <a href="https://arxiv.org/abs/2412.02701">Upper bounds for the prime divisors of friends of 10-II</a>, arXiv:2412.02701 [math.GM], 2024. See p. 8. %H A074902 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FriendlyPair.html">Friendly Pair</a> %H A074902 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FriendlyNumber.html">Friendly Number</a> %e A074902 24 is in the sequence since abundancy(24) = abundancy(91963648) = 5/2. %Y A074902 Union of A050972 and A050973. Cf. A014567. %K A074902 nonn %O A074902 1,1 %A A074902 _N. J. A. Sloane_, Sep 15 2002 %E A074902 Edited by _Dean Hickerson_, Sep 19 2002