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

Author

Bill Moran (moran1(AT)llnl.gov)

Keywords

• nonn
• base
• nice

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.

Crossrefs

Subsequence of A005349, Niven (or Harshad) numbers.

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

Programs

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

Maple

filter:= proc(n) local q;
  q:= n/convert(convert(n,base,10),`+`);
  q::integer and isprime(q)
end proc:
select(filter, [$1..1000]); # Robert Israel, May 13 2025

Mathematica

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

PARI

is(n)=(k->denominator(k)==1&&isprime(k))(n/sumdigits(n)) \\ Charles R Greathouse IV, Jan 10 2014

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

Extensions

Name corrected by Charles R Greathouse IV, Jan 10 2014