cp's OEIS Frontend

A356349 Primitive Niven numbers: terms of A005349 that are not ten times another term of A005349.

%I A356349 #12 Oct 17 2022 07:12:33
%S A356349 1,2,3,4,5,6,7,8,9,12,18,21,24,27,36,42,45,48,54,63,72,81,84,102,108,
%T A356349 110,111,112,114,117,126,132,133,135,140,144,150,152,153,156,162,171,
%U A356349 190,192,195,198,201,204,207,209,216,220,222,224,225,228,230,234
%N A356349 Primitive Niven numbers: terms of A005349 that are not ten times another term of A005349.
%C A356349 A005349(k) belongs to this sequence iff A113315(k) is not a multiple of 10.
%C A356349 This sequence is infinite as it contains A133384 and A199682.
%C A356349 Each Niven number can be uniquely written as a(m)*10^z for some m > 0 and z >= 0.
%C A356349 This sequence contains numbers with k trailing zeros for any k >= 0; for example R(2^k) * 10^k (where R = A002275).
%H A356349 <a href="/index/De#decimal_expansion">Index entries for sequences related to decimal expansion of n</a>
%e A356349 190 is a term as 190 is a Niven number and 19 is not a Niven number.
%e A356349 192 is a term as 192 is a Niven number and 192 is not divisible by 10.
%o A356349 (PARI) is(n, base=10) = my (s=sumdigits(n, base)); n%s==0 && (n%base || (n/base)%s)
%o A356349 (Python)
%o A356349 def ok(n):
%o A356349     sd = sum(map(int, str(n)))
%o A356349     return sd and not n%sd and (n%10 or (n//10)%sd)
%o A356349 print([k for k in range(235) if ok(k)]) # _Michael S. Branicky_, Oct 16 2022
%Y A356349 Cf. A002275, A005349, A113315, A133384, A199682.
%K A356349 nonn,base,easy
%O A356349 1,2
%A A356349 _Bernard Schott_ and _Rémy Sigrist_, Oct 15 2022