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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A347408 A248030 A082292 * A332350 A164857 A326125

Adjacent sequences: A248585 A248586 A248587 * A248589 A248590 A248591

Keyword

nonn

Author

Zhi-Wei Sun, Oct 09 2014

Status

approved