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 A064001 #46 Jan 28 2025 01:47:42
%S A064001 81081,153153,171171,189189,207207,223839,243243,261261,279279,297297,
%T A064001 351351,459459,513513,567567,621621,671517,729729,742203,783783,
%U A064001 793611,812889,837837,891891,908523,960687,999999,1024947,1054053,1072071
%N A064001 Odd abundant numbers not divisible by 5.
%C A064001 Or, odd abundant numbers that do not end in 5.
%C A064001 All terms below 2000000 are divisible by 21 (so by 3). Moreover, except for a few, most are divisible by 231. - _Labos Elemer_, Sep 15 2005 [The least term that is not divisible by 21 is a(908) = 28683369. - _Amiram Eldar_, Jan 27 2025]
%C A064001 An odd abundant number (see A005231) not divisible by 3 nor 5 must have at least 15 distinct prime factors (e.g., 61#/5#*7^2*11*13*17, where # is primorial) and be >= 67#/5#*77 = A047802(3) ~ 2.0*10^25. -- The smallest non-primitive abundant number (cf. A006038) in this sequence is 7*a(1) = 567567 = a(14). - _M. F. Hasler_, Jul 27 2016
%C A064001 There are 26 terms less than 10^6 and a surprising fact is that 18 of them are doublets (cf. A020338). - _Omar E. Pol_, Jan 17 2025
%C A064001 The numbers of terms that do not exceed 10^k, for k = 5, 6, ..., are 1, 26, 290, 3071, 31600, 320948, 3174762, 31693948, ... . Apparently, the asymptotic density of this sequence equals 0.000031... . Therefore, the least term not divisible by 3 that was mentioned above is a(~6*10^20) = 20169691981106018776756331. - _Amiram Eldar_, Jan 27 2025
%D A064001 David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Rev. ed. 1997, p. 169.
%H A064001 David A. Corneth, <a href="/A064001/b064001.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harry J. Smith)
%H A064001 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_329.htm">Puzzle 329. Odd abundant numbers not divided by 2 or 3</a>, The Prime Puzzles and Problems Connection.
%H A064001 Jay L. Schiffman, <a href="http://www.rowan.edu/colleges/csm/departments/math/facultystaff/schiffman/Odd%20Abundant%20Numbers.pdf">Odd Abundant Numbers</a>, Mathematical Spectrum, Volume 37, Number 2 (January 2005), pp 73-75.
%t A064001 Select[ Range[ 1, 10^6, 2 ], DivisorSigma[ 1, # ] - 2# > 0 && Mod[ #, 5 ] != 0 & ]
%t A064001 ta={{0}};Do[g=n;s=DivisorSigma[1, n]-2*n; If[Greater[s, 0]&&!Equal[Mod[n, 2], 0]&& !Equal[Mod[n, 5], 0], Print[n];ta=Append[ta, n]], {n, 1, 2000000}] ta=Delete[ta, 1] (* _Labos Elemer_, Sep 15 2005 *)
%o A064001 (PARI) { n=0; forstep (m=1, 10^9, 2, if (m%5 && sigma(m) > 2*m, write("b064001.txt", n++, " ", m); if (n==1000, break)) ) } \\ _Harry J. Smith_, Sep 05 2009
%Y A064001 Intersection of A005231 and A047201.
%Y A064001 Cf. A006038, A047802, A110585.
%Y A064001 Cf. A020338.
%K A064001 nonn
%O A064001 1,1
%A A064001 _Harvey P. Dale_, Sep 17 2001
%E A064001 More terms from _Robert G. Wilson v_, Sep 28 2001
%E A064001 Further terms from _Labos Elemer_, Sep 15 2005
%E A064001 Entry revised by _N. J. A. Sloane_, Mar 28 2006