cp's OEIS Frontend

A248189 Least positive integer m such that m*n divides sigma(m^2+n^2), where sigma(k) is the sum of all positive divisors of k.

%I A248189 #7 Oct 03 2014 10:04:07
%S A248189 1,1,1,7,2,38,4,81,1,102,868,1,9,3,702,26505,1554,14,3,243,1,650,108,
%T A248189 1833,34542,18,68,186,7252,39,58,736839,1,3108,72,778,210,6,3,4830,
%U A248189 267,2,567,5859,6640,6363,3178412,155771,4964,9
%N A248189 Least positive integer m such that m*n divides sigma(m^2+n^2), where sigma(k) is the sum of all positive divisors of k.
%C A248189 Conjecture: a(n) exists for any n > 0.
%C A248189 See also the comments in A248058.
%H A248189 Zhi-Wei Sun, <a href="/A248189/b248189.txt">Table of n, a(n) for n = 1..100</a>
%e A248189 a(6) = 38 since 6*38 = 228 divides sigma(6^2+38^2) = sigma(1480) = 3420 = 15*228.
%t A248189 Do[m=1; Label[aa]; If[Mod[DivisorSigma[1,m^2+n^2], m*n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 50}]
%o A248189 (PARI)
%o A248189 a(n)=m=1;while(sigma(n^2+m^2)%(m*n),m++);m
%o A248189 n=1;while(n<50,print1(a(n),", ");n++) \\ _Derek Orr_, Oct 03 2014
%Y A248189 Cf. A000203, A248054, A248058, A248123.
%K A248189 nonn
%O A248189 1,4
%A A248189 _Zhi-Wei Sun_, Oct 03 2014