A211821 Numbers with all divisors with additive digital root of 1.

1, 19, 37, 73, 109, 127, 163, 181, 199, 271, 307, 361, 379, 397, 433, 487, 523, 541, 577, 613, 631, 703, 739, 757, 811, 829, 883, 919, 937, 991, 1009, 1063, 1117, 1153, 1171, 1279, 1297, 1369, 1387, 1423, 1459, 1531, 1549, 1567, 1621, 1657, 1693, 1747, 1783

Offset: 1

Author

Jaroslav Krizek, Apr 26 2012

Keywords

• nonn
• base

Comments

All divisors of numbers from this sequence are in this sequence. Likewise, the product of any terms in this sequence is a number that is also in this sequence.

Union of A061237 (prime numbers == 1 (mod 9)) and nonprime numbers A211822.

Subsequence of A017173 (numbers of form 9n+1). - Jaroslav Krizek

For prime numbers, it is enough to verify that the number itself is congruent to 1 mod 9. The first composite term is 361, which is the square of the first prime in this sequence. - Alonso del Arte, May 02 2012

Examples

			Number 703 with divisors 1, 19, 37, 703 is in sequence because all divisors have additive digital root of 1.
		

Crossrefs

Cf. A211822, A211823, A024906, A061237, A017173.

Programs

Mathematica

digitalRoot[n_, b_:10] := FixedPoint[Plus@@IntegerDigits[#, b] &,  n]; A211821 = Select[Range[1, 1999, 9], Union[digitalRoot[Divisors[#]]] == {1} &] (* Alonso del Arte, May 02 2012 *)

Formula

a(n) = 9*k(n) + 1 for k(n) = A211823(n).