A358255 - OEIS

%I #20 Nov 06 2022 07:47:53

%S 110,140,150,190,220,230,280,320,330,370,410,440,460,510,550,640,660,

%T 690,730,770,780,820,870,880,910,960,990,1010,1040,1050,1090,1130,

%U 1160,1180,1220,1230,1270,1300,1310,1360,1380,1410,1450,1540,1590,1630,1680,1720,1740,1770,1810,1860,1890,2020

%N Primitive Niven numbers ending with zero.

%C A primitive Niven number (A356349) is a Niven number (A005349) that is not ten times another Niven number.

%C For any k > 0, there exist terms with k trailing zeros; for example R_2^k * 10^k (where R = A002275), so this sequence is infinite.

%C The smallest primitive Niven number ending with m zeros is A358256(m).

%H Giovanni Resta, <a href="https://www.numbersaplenty.com/set/Harshad_number/">Harshad numbers</a>.

%e 150 is a term as 150 is a Niven number and 15 is not a Niven number.

%e 180 is not a term as 180 is a Niven number but 18 is also a Niven number.

%t Select[10*Range[200], Divisible[#, (s = Plus @@ IntegerDigits[#])] && ! Divisible[#/10, s] &] (* _Amiram Eldar_, Nov 05 2022 *)

%o (PARI) isniven(n) = n%sumdigits(n)==0; \\ A005349

%o isok(m) = !(m % 10) && isniven(m) && !isniven(m/10); \\ _Michel Marcus_, Nov 05 2022

%Y Cf. A002275, A005349.

%Y Intersection of A008592 and A356349.

%K nonn,base

%O 1,1

%A _Bernard Schott_, Nov 05 2022