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

1,1

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).

Links

Table of n, a(n) for n=1..54.

Giovanni Resta, Harshad numbers.

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A002275, A005349.

Intersection of A008592 and A356349.

Sequence in context: A345386 A095611 A335272 * A307534 A200070 A324210

Adjacent sequences: A358252 A358253 A358254 * A358256 A358257 A358258

Keyword

nonn,base

Author

Bernard Schott, Nov 05 2022

Status

approved