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.

5, 5, 22, 44, 85, 85, 230, 260, 352, 950, 950, 1172, 1172, 1172, 1172, 1172, 1172, 1172, 1172, 1901, 1901, 7249, 7249, 7249, 12932, 12932, 12932, 12932, 12932, 38852, 38852, 226324, 226324, 235372, 235372, 235372, 413974, 413974, 423485, 423485

Offset: 1

Author

Labos Elemer, Aug 23 2004

Keywords

• nonn

Comments

It appears that arbitrarily long chains exist.

Examples

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

Crossrefs

Cf. A000203, A084301, A074627.

Programs

Mathematica

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 *)