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A169635 Integers n such that sigma_2(n) = sigma_2(n + 2) where sigma_2(n) is the sum of squares of divisors of n (A001157). 0
24, 215, 280, 1079, 947519, 1362239, 2230271, 14939999, 19720007, 32509439, 45581759, 45841247, 49436927, 78436511, 82842911, 101014631, 166828031, 225622151, 225757799, 250999559, 377129087, 554998751, 619606439, 846765431, 1204092287, 1302170687, 1710035711 (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).

LINKS

Table of n, a(n) for n=1..27.

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.

EXAMPLE

For n=24, sigma_2(24) = sigma_2(26)= 850.

MAPLE

with(numtheory):for n from 1 to 500000000 do:liste:= divisors(n) : s2 :=sum(liste[i]^2, i=1..nops(liste)):liste:=divisors(n+2):s3:=sum(liste[i]^2, i=1..nops(liste)):if s2 = s3 then print(n):else fi:od:

MATHEMATICA

Select[Range[10^9], DivisorSigma[2, #] == DivisorSigma[2, #+2]&]

CROSSREFS

Cf. A000005, A000203, A001158, A001159, A053807, A064602, A175199.

Sequence in context: A097321 A105946 A050222 * A269496 A221434 A008655

Adjacent sequences:  A169632 A169633 A169634 * A169636 A169637 A169638

KEYWORD

nonn

AUTHOR

Michel Lagneau, Apr 04 2010

EXTENSIONS

a(25)-a(27) from Donovan Johnson, Apr 14 2013

STATUS

approved

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Last modified October 16 07:07 EDT 2021. Contains 348041 sequences. (Running on oeis4.)