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).

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

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