A358256 -id:A358256 - cp's OEIS frontend

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

Bernard Schott, Nov 05 2022

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).

			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.

Giovanni Resta, Harshad numbers.

Cf. A002275, A005349.

Intersection of A008592 and A356349.

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

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

A363789 a(n) is the smallest primitive binary Niven number (A363787) whose binary representation is ending with n zeros.

Original entry on oeis.org

1, 6, 60, 2040, 1048560, 137438953440, 1180591620717411303360, 43556142965880123323311949751266331066240, 29642774844752946028434172162224104410437116074403984394101141506025761187823360

Offset: 0

Amiram Eldar, Jun 22 2023

The least term k of A363787 such that A007814(k) = n.
Also, the least binary Niven number (A049445) with a binary weight (A000120) that equals 2^n.
The next term, a(9) = 6.864... * 10^156, is too long to include in the Data section.

Amiram Eldar, Table of n, a(n) for n = 0..11

Subsequence of A049445, A143115 and A363787.

Cf. A000120, A007814, A066524, A358256 (decimal analog).

a[n_] := (2^(2^n)-1) * 2^n; Array[a, 9, 0]

PARI
```
a(n) = (2^(2^n)-1) * 2^n;
```

a(n) = (2^(2^n)-1) * 2^n = A066524(2^n).

a(n) = A143115(2^n).

cp's OEIS Frontend

A358255 Primitive Niven numbers ending with zero.

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