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 A090945 #23 Oct 19 2024 08:34:49 %S A090945 1,140,270,672,1638,2970,6200,8190,18600,18620,27846,30240,32760, %T A090945 55860,105664,117800,167400,173600,237510,242060,332640,360360,539400, %U A090945 695520,726180,753480,950976,1089270,1421280,1539720 %N A090945 Harmonic numbers (A001599) which are not perfect (A000396). %D A090945 Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B2, pp. 74-84. %H A090945 Amiram Eldar, <a href="/A090945/b090945.txt">Table of n, a(n) for n = 1..930</a> (terms below 10^14; terms 1..77 from Muniru A Asiru) %H A090945 T. Goto and S. Shibata, <a href="http://dx.doi.org/10.1090/S0025-5718-03-01554-0">All numbers whose positive divisors have integral harmonic mean up to 300</a>, Math. Comput. 73 (2004), 475-491. %e A090945 A001599(4) = 140, but 336 = sigma(140) <> 2*140 = 280. Thus, 140 is a harmonic number which is not perfect. - _Muniru A Asiru_, Nov 26 2018 %t A090945 Select[Range[2 10^7], IntegerQ[HarmonicMean[Divisors[#]]] && !DivisorSigma[1, #]==2 # &] (* _Vincenzo Librandi_, Nov 27 2018 *) %o A090945 (GAP) Concatenation([1],Filtered([2,4..2000000],n->Sigma(n)<>2*n and IsInt(n*Tau(n)/Sigma(n)))); # _Muniru A Asiru_, Nov 26 2018 %o A090945 (PARI) isok(n) = my(sn = sigma(n)); (frac(n*numdiv(n)/sn) == 0) && (sn != 2*n); \\ _Michel Marcus_, Nov 28 2018 %Y A090945 Cf. A001599, A003601. Different from A007340. %Y A090945 For the associated harmonic means, see A102408. %K A090945 nonn %O A090945 1,2 %A A090945 _N. J. A. Sloane_, Feb 28 2004