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 A211821 Numbers with all divisors with additive digital root of 1. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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 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: A039321 A043144 A043924 * A061237 A158293 A107579 Adjacent sequences:  A211818 A211819 A211820 * A211822 A211823 A211824 KEYWORD nonn,base AUTHOR Jaroslav Krizek, Apr 26 2012 STATUS approved

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