|
%I M5234 #56 Feb 13 2024 06:54:50
%S 33,54,284,366,834,848,918,1240,1504,2910,2913,3304,4148,4187,6110,
%T 6902,7169,7912,9359,10250,10540,12565,15085,17272,17814,19004,19688,
%U 21410,21461,24881,25019,26609,28124,30592,30788,31484,38210,38982,39786,40310,45354
%N Numbers k such that sigma(k+2) = sigma(k).
%C Numbers k such that antisigma(k+2) - antisigma(k) = 2*k + 3, where antisigma(m) = A024816(m) = sum of nondivisors of m. - _Jaroslav Krizek_, Mar 17 2013
%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 33, pp 12, Ellipses, Paris 2008.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Donovan Johnson, <a href="/A007373/b007373.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Zak Seidov)
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H A. Weingartner, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Weingartner/wein3.html">On the Solutions of sigma(n) = sigma(n+k)</a>, Journal of Integer Sequences, Vol. 14 (2011), #11.5.5.
%H R. G. Wilson, V, <a href="/A007015/a007015.pdf">Letter to N. J. A. Sloane, Jul. 1992</a>
%t Flatten[Position[Partition[DivisorSigma[1,Range[300000]],3,1], {x_, _, x_}]] (* _Harvey P. Dale_, Aug 08 2011 *)
%t SequencePosition[DivisorSigma[1,Range[300000]],{x_,_,x_}][[All,1]] (* _Harvey P. Dale_, Nov 17 2022 *)
%o (PARI) je=[]; for(n=1,10^5,a=sigma(n); b=sigma(n+2); if(a==b,je=concat(je,n))); je
%Y Essentially the same as A055574.
%Y Cf. A002961, A015861, A015863, A015865, A015866, A015867, A015876, A015877, A015880, A015881, A015882, A015883, A181647. [From _Reinhard Zumkeller_, Nov 03 2010]
%K nonn
%O 1,1
%A _N. J. A. Sloane_, _Mira Bernstein_, _Robert G. Wilson v_
%E More terms from _Jason Earls_, Jul 20 2001
|
