cp's OEIS Frontend

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

%I A248588 #17 Mar 08 2024 11:59:35
%S A248588 2,12,4,9,40,6,8,10,15,14,21,112,27,22,16,12,39,289,65,34,18,20,57,60,
%T A248588 95,46,69,28,115,96,32,58,45,62,93,24,155,340,217,44,63,30,50,82,123,
%U A248588 52,129,204,75,40,141,228,235,42,36,106,99,68,265,120
%N A248588 Least positive integer m such that m + n divides sigma(m), where sigma(m) is the sum of all positive divisors of m.
%C A248588 Conjecture: a(n) exists for any n > 0.
%H A248588 Zhi-Wei Sun, <a href="/A248588/b248588.txt">Table of n, a(n) for n = 1..10000</a>
%e A248588 a(5) = 40 since 40 + 5 = 45 divides sigma(40) =  90.
%e A248588 a(1162) = 24031232 since 24031232 + 1162 = 24032394 divides sigma(24031232) =  48064788 = 2*24032394.
%t A248588 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}]
%t A248588 lpi[n_]:=Module[{m=1},While[!Divisible[DivisorSigma[1,m],m+n],m++];m]; Array[lpi,60] (* _Harvey P. Dale_, Feb 21 2020 *)
%o A248588 (PARI) a(n) = my(m = 1); while(sigma(m) % (m+n), m++); m; \\ _Michel Marcus_, Aug 08 2017
%Y A248588 Cf. A000203, A248007, A248008, A248029, A248030, A248568, A248590.
%K A248588 nonn
%O A248588 1,1
%A A248588 _Zhi-Wei Sun_, Oct 09 2014