A097016 - OEIS

A097016

a(n)=x is the first term in chain of consecutive integers, for all of which the value of sigma[x] is divisible by 6.

%I #5 Mar 06 2018 23:06:02

%S 5,5,22,44,85,85,230,260,352,950,950,1172,1172,1172,1172,1172,1172,

%T 1172,1172,1901,1901,7249,7249,7249,12932,12932,12932,12932,12932,

%U 38852,38852,226324,226324,235372,235372,235372,413974,413974,423485,423485

%N a(n)=x is the first term in chain of consecutive integers, for all of which the value of sigma[x] is divisible by 6.

%C It appears that arbitrarily long chains exist.

%e n=52: a(52)=1270685 means that all entries in {sigma[a(52)],...,sigma[1270685+52-1]} ={1666224,...,2520672} are divisible by 6.

%t With[{ds=Table[If[Divisible[DivisorSigma[1,n],6],1,0],{n,450000}]},Flatten[ Table[SequencePosition[ds,PadRight[{},n,1],1],{n,40}],1][[All,1]]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 06 2018 *)

%Y Cf. A000203, A084301, A074627.

%K nonn

%O 1,1

%A _Labos Elemer_, Aug 23 2004