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 A175199 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). 2
 24, 430, 645, 860, 120, 864, 168, 1720, 1935, 10790, 264, 2580, 2795, 1570, 16185, 3440, 408, 3870, 456, 21580, 2355, 4730, 552, 5160, 600, 5590, 5805, 3140, 696, 4320, 744, 6880, 7095, 1248, 840, 7740, 888, 8170, 8385, 43160, 984, 4710, 1032, 9460 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The equation sigma_2(n) = sigma_2(n + p) has infinitely many solutions where p >= 2 and p is even (J. M. De Koninck). REFERENCES 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. T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 38. LINKS Amiram Eldar, Table of n, a(n) for n = 1..1000 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. J. M. De Koninck, On the solutions of sigma2(n) = sigma2(n + p), Ann. Univ. Sci. Budapest Sect. Comput. 21 (2002), 127-133. Eric Weisstein's World of Mathematics, Divisor Function. EXAMPLE 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. MAPLE 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: CROSSREFS Cf. A000005, A000203, A001158, A001159. Cf. A053807, A064602. Sequence in context: A072975 A062193 A016268 * A051546 A209448 A264504 Adjacent sequences: A175196 A175197 A175198 * A175200 A175201 A175202 KEYWORD nonn AUTHOR Michel Lagneau, Mar 03 2010 STATUS approved

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Last modified September 27 08:15 EDT 2023. Contains 365674 sequences. (Running on oeis4.)