A001101 Moran numbers: k such that k/(sum of digits of k) is prime.

18, 21, 27, 42, 45, 63, 84, 111, 114, 117, 133, 152, 153, 156, 171, 190, 195, 198, 201, 207, 209, 222, 228, 247, 261, 266, 285, 333, 370, 372, 399, 402, 407, 423, 444, 465, 481, 511, 516, 518, 531, 555, 558, 592, 603

Offset

1,1

Comments

Witno conjectures that a(n) ~ c*n log(n)^2 for some c. - Charles R Greathouse IV, Jul 26 2011

References

Bill Moran, Problem 2074: The Moran Numbers, J. Rec. Math., Vol. 25 No. 3, pp. 215, 1993.

Links

Aaron Toponce, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Amin Witno, Numbers which factor as their digital sum times a prime, International Journal of Open Problems in Computer Science and Mathematics 3:2 (2010), pp. 132-136.

Mathematica

Select[Range[700], PrimeQ[ # / Total[IntegerDigits[#]]]&] (* Jean-François Alcover, Nov 30 2011 *)

Prog

(Haskell)
import Data.List (findIndices)
a001101 n = a001101_list !! (n-1)
a001101_list = map succ $ findIndices p [1..] where
   p n = m == 0 && a010051 n' == 1 where
      (n', m) = divMod n (a007953 n)
-- Reinhard Zumkeller, Jun 16 2011
(PARI) is(n)=(k->denominator(k)==1&&isprime(k))(n/sumdigits(n)) \\ Charles R Greathouse IV, Jan 10 2014
(Python)
# 1000000 primes: https://primes.utm.edu/lists/small/millions/primes1.zip
# "primes1.txt" must be formatted as a b-file before execution
import csv
with open("primes1.txt", "r") as f:
....reader = csv.reader(f, delimiter=" ")
....primes = set([int(rows[1]) for rows in reader])
i, n = 1, 1
with open("b001101.txt", "w") as f:
....while i <= 10000:
........if n % sum(map(int, str(n))) == 0 and n/sum(map(int, str(n))) in primes:
............f.write("{} {}\n".format(i, n))
............i += 1
........n += 1
# Aaron Toponce, Feb 14 2018
(Python)
from sympy import isprime
def ok(n): s = sum(map(int, str(n))); return s and n%s==0 and isprime(n//s)
print([k for k in range(604) if ok(k)]) # Michael S. Branicky, Mar 28 2022

Crossrefs

Subsequence of A005349, Niven (or Harshad) numbers.

Cf. A007953, A010051, A085775, A108780, A130338, A062339.

Sequence in context: A216295 A217058 A172052 * A088341 A105145 A244603

Adjacent sequences: A001098 A001099 A001100 * A001102 A001103 A001104

Keyword

nonn,base,nice

Author

Bill Moran (moran1(AT)llnl.gov)

Extensions

Name corrected by Charles R Greathouse IV, Jan 10 2014

Status

approved