A245802 Numbers that are divisible by the sum of their base 8 digits.

1, 2, 3, 4, 5, 6, 7, 8, 14, 16, 21, 24, 28, 32, 35, 40, 42, 48, 49, 56, 64, 66, 70, 72, 75, 77, 84, 88, 90, 91, 98, 105, 112, 120, 126, 128, 129, 132, 133, 135, 140, 144, 145, 147, 150, 154, 161, 165, 168, 176, 180, 182, 192, 196, 198, 200, 203, 210, 216, 217

Offset: 1

Author

Chai Wah Wu, Aug 22 2014

Keywords

• nonn
• base

Comments

A base 8 version of Harshad (or Niven) numbers (A005349).

Numbers n such that n = 0 modulo A053829(n), where the latter sequence gives the sum of digits when n is represented in the octal number system. - Antti Karttunen, Aug 22 2014

Examples

			36971 is in the sequence as it is 110153 in octal and 1 + 1 + 0 + 1 + 5 + 3 = 11 which divides 36971.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to octal numbers

Crossrefs

Cf. A005349, A053829, A241989.

Programs

Mathematica

Select[Range[256], IntegerQ[#/(Plus@@IntegerDigits[#, 8])] &] (* Alonso del Arte, Aug 26 2014 *)

Python

from gmpy2 import digits
A245802 = [n for n in range(1,10**3) if not n % sum([int(d) for d in digits(n,8)])]
(MIT/GNU Scheme, with Antti Karttunen's IntSeq-library)
(define A245802 (MATCHING-POS 1 1 (lambda (n) (zero? (modulo n (A053829 n))))))
(define (A053829 n) (let loop ((n n) (i 0)) (if (zero? n) i (loop (floor->exact (/ n 8)) (+ i (modulo n 8))))))