A211823 Numbers k such that 9*k+1 are numbers with all divisors with additive digital root = 1.

0, 2, 4, 8, 12, 14, 18, 20, 22, 30, 34, 40, 42, 44, 48, 54, 58, 60, 64, 68, 70, 78, 82, 84, 90, 92, 98, 102, 104, 110, 112, 118, 124, 128, 130, 142, 144, 152, 154, 158, 162, 170, 172, 174, 180, 184, 188, 194, 198, 200, 208, 222, 224, 228, 230, 232, 238, 240, 242

Offset: 1

Author

Jaroslav Krizek, Apr 26 2012

Keywords

• nonn
• base

Comments

Numbers of form 9*k+1 with all divisors with digital root = 1 is in A211821.

Supersequence of A024906 (numbers n such that 9*n+1 is prime).

Examples

			Number k = 40 is in sequence because number 9*40 + 1 = 361 is number with all divisors (1, 19, 361) with additive digital root = 1.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A211821, A024906, A061237, A017173, A211822

Programs

Mathematica

adrQ[n_]:=NestWhile[Total[IntegerDigits[#]]&,n,#>9&]==1; Select[Range[ 0,250],AllTrue[Divisors[9#+1],adrQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 27 2020 *)

Extensions

Corrected (230 inserted) by Harvey P. Dale, Aug 27 2020