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.

1, 1, 1, 7, 2, 38, 4, 81, 1, 102, 868, 1, 9, 3, 702, 26505, 1554, 14, 3, 243, 1, 650, 108, 1833, 34542, 18, 68, 186, 7252, 39, 58, 736839, 1, 3108, 72, 778, 210, 6, 3, 4830, 267, 2, 567, 5859, 6640, 6363, 3178412, 155771, 4964, 9

Offset: 1

Author

Zhi-Wei Sun, Oct 03 2014

Keywords

• nonn

Comments

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

See also the comments in A248058.

Examples

			a(6) = 38 since 6*38 = 228 divides sigma(6^2+38^2) = sigma(1480) = 3420 = 15*228.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000203, A248054, A248058, A248123.

Programs

Mathematica

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}]

PARI

a(n)=m=1;while(sigma(n^2+m^2)%(m*n),m++);m
n=1;while(n<50,print1(a(n),", ");n++) \\ Derek Orr, Oct 03 2014