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
KEYWORD
nonn,base,nice
AUTHOR
Bill Moran (moran1(AT)llnl.gov)
EXTENSIONS
Name corrected by Charles R Greathouse IV, Jan 10 2014
STATUS
approved