A064150 Numbers divisible by the sum of their ternary digits.

1, 2, 3, 4, 6, 8, 9, 10, 12, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 33, 35, 36, 39, 40, 45, 48, 54, 56, 57, 60, 63, 64, 65, 72, 75, 77, 78, 80, 81, 82, 84, 87, 88, 90, 92, 93, 95, 96, 99, 100, 105, 108, 111, 112, 115, 117, 120, 132, 133, 135, 136, 144, 145, 150, 152

Offset: 1

Author

Len Smiley, Sep 11 2001

Keywords

• base
• easy
• nonn
• nice

Comments

a(n) mod A053735(a(n)) = 0. - Reinhard Zumkeller, Nov 25 2009

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith).
• Paul Dahlenberg and Tom Edgar, Consecutive factorial base Niven numbers, Fibonacci Quarterly, Vol. 56, No. 2 (2018), pp. 163-166.

Crossrefs

Cf. A005349 (Decimal), A049445 (Binary).

Programs

Haskell

a064150 n = a064150_list !! (n-1)
a064150_list = filter (\x -> x `mod` a053735 x == 0) [1..]
-- Reinhard Zumkeller, Oct 28 2012

Mathematica

Select[Range[200], IntegerQ[#/(Plus@@IntegerDigits[#, 3])] &] (* Alonso del Arte, May 27 2011 *)

PARI

isok(m)={m % sumdigits(m, 3) == 0} \\ Harry J. Smith, Sep 09 2009

Python

import numpy as np
def gen():
    for dec_num in range(1,153):
        tern_num = np.base_repr(dec_num, 3)
        sum_tern_digits = 0
        for i in tern_num:
            sum_tern_digits += int(i)
        if dec_num % sum_tern_digits == 0:
            yield dec_num
print(list((gen()))) # Adrienne Leonardo, Dec 28 2024

Extensions

Corrected and extended by Vladeta Jovovic, Sep 22 2001

Offset corrected by Reinhard Zumkeller, Oct 28 2012