cp's OEIS Frontend

A285829 Numbers n such that, for any i and j with i >= j >= 0, ds^i(n) divides ds^j(n) (where ds^k denotes the k-th iteration of the digital sum).

%I A285829 #6 Apr 28 2017 07:37:15
%S A285829 1,2,3,4,5,6,7,8,9,10,12,18,20,21,24,27,30,36,40,42,45,48,50,54,60,63,
%T A285829 70,72,80,81,84,90,100,102,108,110,111,112,114,117,120,126,132,133,
%U A285829 135,140,144,150,152,153,156,162,171,180,190,192,198,200,201,204,207,210,216,220,222,224,225,228,230,234,240,243,252,261,264,270,280,288,300,306,312
%N A285829 Numbers n such that, for any i and j with i >= j >= 0, ds^i(n) divides ds^j(n) (where ds^k denotes the k-th iteration of the digital sum).
%C A285829 All terms are Niven numbers (A005349).
%C A285829 All terms belongs to A234474; the first difference occurs at index 81: a(81) = 312 whereas A234474(81) = 308.
%C A285829 All powers of 10 belong to the sequence, hence the sequence is infinite.
%H A285829 Rémy Sigrist, <a href="/A285829/b285829.txt">Table of n, a(n) for n = 1..10000</a>
%e A285829 The digital sum of 312 is 6, and it divides 312; the digital sum of 6 is 6; hence 312 appears in the sequence.
%e A285829 The digital sum of 308 is 11, which divides 308; however the digital sum of 11 is 2, which does not divide 11; hence 308 is not in the sequence.
%o A285829 (PARI) is(n) = my (d=sumdigits(n)); if (n==d, return (1)); if (n%d, return (0)); return (is(d))
%Y A285829 Cf. A005349, A234474.
%K A285829 nonn,base
%O A285829 1,2
%A A285829 _Rémy Sigrist_, Apr 27 2017