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A175199
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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).
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2
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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
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OFFSET
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1,1
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COMMENTS
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The equation sigma_2(n) = sigma_2(n + p) has infinitely many solutions where p >= 2 and p is even (J. M. De Koninck).
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REFERENCES
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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.
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LINKS
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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].
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EXAMPLE
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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.
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MAPLE
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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:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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