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A001101 Moran numbers: n such that (n / sum of digits of n) is prime. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A005349, Niven (or Harshad) numbers.

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.

MAPLE

P:=proc(n) local a; a:=n/convert(convert(n, base, 10), `+`);

if frac(a)=0 then if isprime(a) then n; fi; fi;

end: seq(P(i), i=1..10^3); # Paolo P. Lava, Feb 05 2018

MATHEMATICA

Select[Range[700], PrimeQ[ # / Total[IntegerDigits[#]]]&] (* Jean-Fran├žois 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

CROSSREFS

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

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Last modified April 23 01:13 EDT 2018. Contains 302916 sequences. (Running on oeis4.)