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%I #14 Aug 03 2014 14:37:26
%S 1,19,37,73,109,127,163,181,199,271,307,361,379,397,433,487,523,541,
%T 577,613,631,703,739,757,811,829,883,919,937,991,1009,1063,1117,1153,
%U 1171,1279,1297,1369,1387,1423,1459,1531,1549,1567,1621,1657,1693,1747,1783
%N Numbers with all divisors with additive digital root of 1.
%C 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.
%C Union of A061237 (prime numbers == 1 (mod 9)) and nonprime numbers A211822.
%C Subsequence of A017173 (numbers of form 9n+1). - Krizek
%C 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
%F a(n) = 9*k(n) + 1 for k(n) = A211823(n).
%e Number 703 with divisors 1, 19, 37, 703 is in sequence because all divisors have additive digital root of 1.
%t 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 *)
%Y Cf. A211822, A211823, A024906, A061237, A017173.
%K nonn,base
%O 1,2
%A _Jaroslav Krizek_, Apr 26 2012
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