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.

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, 28, 27, 75, 41, 16, 78, 44, 6, 23, 14, 207, 59, 21, 84, 17, 78, 7, 3, 11725, 10, 5, 2, 1669, 361, 134, 10, 141, 310, 21, 73, 21, 33, 38, 121

Offset: 1

Author

Zhi-Wei Sun, Sep 30 2014

Keywords

• nonn

Comments

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

Examples

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

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..3190
• Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685, 2014.

Crossrefs

Cf. A000203, A248008, A248036, A248052.

Programs

Mathematica

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}]