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A248588 Least positive integer m such that m + n divides sigma(m), where sigma(m) is the sum of all positive divisors of m. 4
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 (list; graph; refs; listen; history; text; internal format)
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.

MAPLE

with(numtheory): P:=proc(q) local k; for k from 1 to infinity do

if sigma(k) mod (q+k)=0 then break; fi; od; k; end: seq(P(i), i=1..100);

# Paolo P. Lava, Aug 08 2017

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

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Last modified October 3 22:17 EDT 2022. Contains 357237 sequences. (Running on oeis4.)