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 A319735 #26 Feb 16 2025 08:33:56 %S A319735 70,4030,5830,4199030,1550860550,66072609790 %N A319735 Primitive weird numbers (pwn; A002975) congruent to 2 mod 4. %C A319735 Primitive weird numbers divisible by 2 but not by 4. %C A319735 10805836895078390 = 2 * 5 * 11 * 89 * 167 * 829 * 7972687 is a term. %D A319735 Gianluca Amato, Maximilian F. Hasler, Giuseppe Melfi, Maurizio Parton. Primitive weird numbers having more than three distinct prime factors. Rivista di Matematica della Università degli studi di Parma, 2016, 7(1), pp. 153-163. (hal-01684543) %H A319735 G. Amato, M. Hasler, G. Melfi and M. Parton, <a href="http://rivista.math.unipr.it/vols/2016-7-1/amato-et-al.html">Primitive weird numbers having more than three distinct prime factors</a>, Riv. Mat. Univ. Parma, Vol. 7, No. 1 (2016) 153-163. %H A319735 Gianluca Amato, Maximilian F. Hasler, Giuseppe Melfi, Maurizio Parton, <a href="https://arxiv.org/abs/1802.07178">Primitive abundant and weird numbers with many prime factors</a>, arXiv:1802.07178 [math.NT], 2018. %H A319735 Stan Benkoski, <a href="http://www.jstor.org/stable/2316276">Problem E2308</a>, Amer. Math. Monthly, 79 (1972) 774. %H A319735 S. J. Benkoski and P. Erdos, <a href="http://dx.doi.org/10.1090/S0025-5718-1974-0347726-9">On weird and pseudoperfect numbers</a>, Math. Comp., 28 (1974), pp. 617-623. <a href="http://www.renyi.hu/~p_erdos/1974-24.pdf">Alternate link</a>; <a href="http://dx.doi.org/10.1090/S0025-5718-1975-0360452-6">1975 corrigendum</a>. %H A319735 R. K. Guy, <a href="/A001599/a001599_1.pdf">Letter to N. J. A. Sloane with attachment, Jun. 1991</a>. %H A319735 Douglas E. Iannucci, <a href="http://arxiv.org/abs/1504.02761">On primitive weird numbers of the form 2^k*p*q</a>, arXiv:1504.02761 [math.NT], 2015. %H A319735 Giuseppe Melfi, <a href="http://dx.doi.org/10.1016/j.jnt.2014.07.024">On the conditional infiniteness of primitive weird numbers</a>, Journal of Number Theory, Volume 147, February 2015, Pages 508-514. %H A319735 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WeirdNumber.html">Weird Number</a>. %H A319735 Wikipedia, <a href="http://en.wikipedia.org/wiki/Weird_number">Weird number</a> %e A319735 a(1) is 70 = 2 * 5 * 7 with abundance of 4; %e A319735 a(2) is 4030 = 2 * 5 * 13 * 31 with abundance of 4; %e A319735 a(3) is 5830 = 2 * 5 * 11 * 53 with abundance of 4; %e A319735 a(4) is 4199030 = 2 * 5 * 11 * 59 * 647 with abundance of 20; %e A319735 a(5) is 1550860550 = 2 * 5^2 * 29 * 37 * 137 * 211 with abundance of 20; %e A319735 a(6) is 66072609790 = 2 * 5 * 11 * 127^2 * 167 * 223 with abundance of 4; etc. %e A319735 From _M. F. Hasler_, Nov 28 2018: (Start) %e A319735 The larger terms are in other sequences related to PWN with many prime factors. We have the following relations: %e A319735 a(3) = 70 = A258882(1) = A258374(3) = A258250(1) = A002975(1). %e A319735 a(3) = 4030 = A258883(1) = A258374(4) = A258401(1) = A258250(3) = A002975(3). %e A319735 a(3) = 5830 = A258883(2) = A258401(2) = A258250(4) = A002975(4). %e A319735 a(4) = 4199030 = A258884(1) = A258374(5) = A258401(11) = A265727(15). %e A319735 a(5) = 1550860550 = A258885(1) = A273815(1) = A258374(6). %e A319735 a(6) = 66072609790 = A258885(3) = A273815(3). (End) %t A319735 (* import the b-file in A002975 and assign it to lst *); %t A319735 Select[lst, IntegerExponent[#, 2] == 1 &] %Y A319735 Cf. A002975, A258375, A258401, A258882, A258883, A258884, A258885. %K A319735 nonn,more %O A319735 1,1 %A A319735 _M. F. Hasler_ and _Robert G. Wilson v_, Sep 26 2018