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A372114 Sum of squares of divisors of the numbers m such that m and m+2 have the same sum of squares of divisors.

%I A372114 #16 May 30 2025 08:02:35
%S A372114 850,48100,110500,1171300,897826072900,1855703820100,4974132151300,
%T A372114 223203708201604,388880538297700,1056863959716100,2077699792101700,
%U A372114 2101425630304900,2444010061663300,6152287246125700,6862948725741700,10203957350659300,27831593408440900,50905357902220900
%N A372114 Sum of squares of divisors of the numbers m such that m and m+2 have the same sum of squares of divisors.
%C A372114 All the terms are even.
%C A372114 There are only 2 equal consecutive terms in A001157: sigma_2(6) = sigma_2(7) = 50.
%H A372114 Amiram Eldar, <a href="/A372114/b372114.txt">Table of n, a(n) for n = 1..156</a>
%H A372114 Jean-Marie De Koninck, <a href="https://ac.inf.elte.hu/Vol_021_2002/doi/127_21.pdf">On the solutions of sigma_2(n) = sigma_2(n + l)</a>, Ann. Univ. Sci. Budapest Sect. Comput. 21 (2002), 127-133.
%F A372114 a(n) = A001157(A169635(n)).
%t A372114 seq[mmax_] := Module[{s1 = DivisorSigma[2, 1], s2 = DivisorSigma[2, 2], s3, s4, s={}}, Do[s3 = DivisorSigma[2, m]; s4 = DivisorSigma[2, m+1]; If[s1 == s3, AppendTo[s, s1]]; If[s2 == s4, AppendTo[s, s2]]; s1 = s3; s2 = s4, {m, 3, mmax, 2}]; s]; seq[10^6]
%o A372114 (PARI) lista(mmax) = {my(s1 = sigma(1, 2), s2 = sigma(2, 2), s3, s4); forstep(m = 3, mmax, 2, s3 = sigma(m, 2); s4 = sigma(m+1, 2); if(s1 == s3, print1(s1, ", ")); if(s2 == s4, print1(s2, ", ")); s1 = s3; s2 = s4);}
%Y A372114 Cf. A001157, A169635.
%Y A372114 Similar sequences: A053215, A053249.
%K A372114 nonn
%O A372114 1,1
%A A372114 _Amiram Eldar_, Apr 19 2024