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

1,4

Comments

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

See also the comments in A248058.

Links

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

Example

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

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}]

Prog

(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

Crossrefs

Cf. A000203, A248054, A248058, A248123.

Sequence in context: A282799 A222555 A246799 * A096040 A038268 A100983

Adjacent sequences: A248186 A248187 A248188 * A248190 A248191 A248192

Keyword

nonn

Author

Zhi-Wei Sun, Oct 03 2014

Status

approved