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

1,2

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). - 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

Links

Table of n, a(n) for n=1..49.

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A043144 A043924 A301617 * A061237 A158293 A107579

Adjacent sequences: A211818 A211819 A211820 * A211822 A211823 A211824

Keyword

nonn,base

Author

Jaroslav Krizek, Apr 26 2012

Status

approved