A245802 -id:A245802 - cp's OEIS frontend

A241989 Positive numbers n that are divisible by the sum of the digits of n in base 16.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 30, 32, 33, 35, 36, 40, 45, 48, 50, 54, 60, 64, 65, 66, 70, 72, 75, 80, 90, 96, 99, 100, 105, 108, 112, 120, 126, 128, 130, 132, 135, 140, 144, 150, 160, 165, 175, 176, 180, 192, 195, 198, 200

Offset: 1

Chai Wah Wu, Aug 22 2014

A base 16 version of Harshad (or Niven) numbers (A005349).

Numbers n such that n = 0 modulo A053836(n). - Antti Karttunen, Aug 22 2014

			82478 is in the sequence as it is 1422E in hexadecimal and 1+4+2+2+14 = 23 which divides 82478.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A005349, A053836, A245802.

Select[Range[200], Divisible[#, Total@ IntegerDigits[#, 16]] &] (* Indranil Ghosh, Jun 12 2017 *)

from gmpy2 import digits
A241989 = [n for n in range(1,10**3) if not n % sum([int(d,16) for d in digits(n,16)])]
(MIT/GNU Scheme, with Antti Karttunen's IntSeq-library)
(define A241989 (MATCHING-POS 1 1 (lambda (n) (zero? (modulo n (A053836 n))))))
(define (A053836 n) (let loop ((n n) (i 0)) (if (zero? n) i (loop (floor->exact (/ n 16)) (+ i (modulo n 16))))))

A325309 Square array read by downward antidiagonals: A(n, k) is the k-th Niven number (or Harshad number) in base n.

Original entry on oeis.org

1, 2, 1, 4, 2, 1, 6, 3, 2, 1, 8, 4, 3, 2, 1, 10, 6, 4, 3, 2, 1, 12, 8, 6, 4, 3, 2, 1, 16, 9, 8, 5, 4, 3, 2, 1, 18, 10, 9, 6, 5, 4, 3, 2, 1, 20, 12, 12, 8, 6, 5, 4, 3, 2, 1, 21, 15, 16, 10, 10, 6, 5, 4, 3, 2, 1, 24, 16, 18, 12, 12, 7, 6, 5, 4, 3, 2, 1, 32, 18

Offset: 2

Felix Fröhlich, Sep 06 2019

			The array starts as follows:
1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 21, 24, 32, 34, 36, 40, 42, 48, 55, 60
1, 2, 3, 4, 6,  8,  9, 10, 12, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32
1, 2, 3, 4, 6,  8,  9, 12, 16, 18, 20, 21, 24, 28, 30, 32, 33, 35, 36, 40
1, 2, 3, 4, 5,  6,  8, 10, 12, 15, 16, 18, 20, 24, 25, 26, 27, 28, 30, 32
1, 2, 3, 4, 5,  6, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 42, 44, 45, 48
1, 2, 3, 4, 5,  6,  7,  8,  9, 12, 14, 15, 16, 18, 21, 24, 27, 28, 30, 32
1, 2, 3, 4, 5,  6,  7,  8, 14, 16, 21, 24, 28, 32, 35, 40, 42, 48, 49, 56
1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 12, 16, 18, 20, 24, 27, 28, 30, 32, 36
1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42
1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 15, 20, 22, 24, 25, 30, 33, 35
1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 22, 24, 33, 36, 44, 48, 55, 60
1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 18, 24, 26, 27
1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 26, 28, 39, 42, 52, 56
1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 21, 28, 30, 32
1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 30, 32
1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 24
1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 34, 36

Wikipedia, Harshad number

Cf. A049445 (row 2), A064150 (row 3), A064438 (row 4), A064481 (row 5), A245802 (row 8), A005349 (row 10).

Cf. A005349.

row(n, terms) = my(i=0); for(x=1, oo, if(i >= terms, break); if(x%sumdigits(x, n)==0, print1(x, ", "); i++))
array(rows, cols) = for(x=2, rows+1, row(x, cols); print(""))
array(18, 20) \\ Print initial 18 rows and 20 columns of array

cp's OEIS Frontend

A241989 Positive numbers n that are divisible by the sum of the digits of n in base 16.

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