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 A248054 Least positive integer m such that m + n divides sigma(m^2) + sigma(n^2), where sigma(k) is the sum of all positive divisors of k. 4

%I

%S 1,3,2,7,24,34,3,81,209,16,63,25,7,20,140,10,3,10,22,2,39,4,35,5,4,2,

%T 28,27,75,41,16,78,44,6,23,14,207,59,21,84,17,78,7,3,11725,10,5,2,

%U 1669,361,134,10,141,310,21,73,21,33,38,121

%N Least positive integer m such that m + n divides sigma(m^2) + sigma(n^2), where sigma(k) is the sum of all positive divisors of k.

%C Conjecture: a(n) exists for any n > 0.

%H Zhi-Wei Sun, <a href="/A248054/b248054.txt">Table of n, a(n) for n = 1..3190</a>

%H Zhi-Wei Sun, <a href="http://arxiv.org/abs/1409.5685">A new theorem on the prime-counting function</a>, arXiv:1409.5685, 2014.

%e a(4) = 7 since 7 + 4 = 11 divides sigma(7^2) + sigma(4^2) = 57 + 31 = 88.

%t Do[m=1;Label[aa];If[Mod[DivisorSigma[1,m^2]+DivisorSigma[1,n^2],m+n]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,60}]

%Y Cf. A000203, A248008, A248036, A248052.

%K nonn

%O 1,2

%A _Zhi-Wei Sun_, Sep 30 2014

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Last modified January 21 16:47 EST 2020. Contains 331114 sequences. (Running on oeis4.)