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%I #20 Jul 23 2019 03:25:54
%S 24,430,645,860,120,864,168,1720,1935,10790,264,2580,2795,1570,16185,
%T 3440,408,3870,456,21580,2355,4730,552,5160,600,5590,5805,3140,696,
%U 4320,744,6880,7095,1248,840,7740,888,8170,8385,43160,984,4710,1032,9460
%N Smallest integer n such that sigma_2(n) = sigma_2(n + 2k), k = 1,2,3,.... where sigma_2(n) is the sum of squares of divisors of n (A001157).
%C The equation sigma_2(n) = sigma_2(n + p) has infinitely many solutions where p >= 2 and p is even (J. M. De Koninck).
%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. 827.
%D T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 38.
%H Amiram Eldar, <a href="/A175199/b175199.txt">Table of n, a(n) for n = 1..1000</a>
%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 J. M. De Koninck, <a href="http://ac.inf.elte.hu/Vol_021_2002/127.pdf">On the solutions of sigma2(n) = sigma2(n + p)</a>, Ann. Univ. Sci. Budapest Sect. Comput. 21 (2002), 127-133.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DivisorFunction.html">Divisor Function.</a>
%e For k=1, sigma_2(24) = sigma_2(26)= 850 for k=2, sigma_2(430) = sigma_2(434)= 240500 for k=3, sigma_2(645) = sigma_2(651) = 481000.
%p with(numtheory):for k from 2 by 2 to 200 do :indic:=0:for n from 1 to 100000 do:liste:= divisors(n) : s2 :=sum(liste[i]^2, i=1..nops(liste)):liste:=divisors(n+k):s3:=sum(liste[i]^2, i=1..nops(liste)):if s2 = s3 and indic=0 then print(k):print(n):indic:=1:else fi:od:od:
%Y Cf. A000005, A000203, A001158, A001159.
%Y Cf. A053807, A064602.
%K nonn
%O 1,1
%A _Michel Lagneau_, Mar 03 2010
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