A358255 Primitive Niven numbers ending with zero.

110, 140, 150, 190, 220, 230, 280, 320, 330, 370, 410, 440, 460, 510, 550, 640, 660, 690, 730, 770, 780, 820, 870, 880, 910, 960, 990, 1010, 1040, 1050, 1090, 1130, 1160, 1180, 1220, 1230, 1270, 1300, 1310, 1360, 1380, 1410, 1450, 1540, 1590, 1630, 1680, 1720, 1740, 1770, 1810, 1860, 1890, 2020

Offset: 1

Author

Bernard Schott, Nov 05 2022

Keywords

• nonn
• base

Comments

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

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.

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

Examples

			150 is a term as 150 is a Niven number and 15 is not a Niven number.
180 is not a term as 180 is a Niven number but 18 is also a Niven number.
		

Links

• Giovanni Resta, Harshad numbers.

Crossrefs

Cf. A002275, A005349.

Intersection of A008592 and A356349.

Programs

Mathematica

Select[10*Range[200], Divisible[#, (s = Plus @@ IntegerDigits[#])] && ! Divisible[#/10, s] &] (* Amiram Eldar, Nov 05 2022 *)

PARI

isniven(n) = n%sumdigits(n)==0; \\ A005349
isok(m) = !(m % 10) && isniven(m) && !isniven(m/10); \\ Michel Marcus, Nov 05 2022