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 A001101 Moran numbers: n such that (n / sum of digits of n) is prime. 18
 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 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-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 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

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Last modified October 21 16:40 EDT 2020. Contains 337918 sequences. (Running on oeis4.)