A248588 Least positive integer m such that m + n divides sigma(m), where sigma(m) is the sum of all positive divisors of m.

2, 12, 4, 9, 40, 6, 8, 10, 15, 14, 21, 112, 27, 22, 16, 12, 39, 289, 65, 34, 18, 20, 57, 60, 95, 46, 69, 28, 115, 96, 32, 58, 45, 62, 93, 24, 155, 340, 217, 44, 63, 30, 50, 82, 123, 52, 129, 204, 75, 40, 141, 228, 235, 42, 36, 106, 99, 68, 265, 120

Offset: 1

Author

Zhi-Wei Sun, Oct 09 2014

Keywords

• nonn

Comments

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

Examples

			a(5) = 40 since 40 + 5 = 45 divides sigma(40) =  90.
a(1162) = 24031232 since 24031232 + 1162 = 24032394 divides sigma(24031232) =  48064788 = 2*24032394.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A248007, A248008, A248029, A248030, A248568, A248590.

Programs

Mathematica

Do[m=1;Label[aa];If[Mod[DivisorSigma[1,m],m+n]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,60}]
lpi[n_]:=Module[{m=1},While[!Divisible[DivisorSigma[1,m],m+n],m++];m]; Array[lpi,60] (* Harvey P. Dale, Feb 21 2020 *)

PARI

a(n) = my(m = 1); while(sigma(m) % (m+n), m++); m; \\ Michel Marcus, Aug 08 2017