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 A001101 Moran numbers: n such that floor(n / sum of digits of n) is prime. 5

%I

%S 18,21,27,42,45,63,84,111,114,117,133,152,153,156,171,190,195,198,201,

%T 207,209,222,228,247,261,266,285,333,370,372,399,402,407,423,444,465,

%U 481,511,516,518,531,555,558,592,603

%N Moran numbers: n such that floor(n / sum of digits of n) is prime.

%C Subsequence of A005349, Niven (or Harshad) numbers.

%C Witno conjectures that a(n) ~ c n log(n)^2 for some c. [_Charles R Greathouse IV_, Jul 26 2011]

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

%H T. D. Noe, <a href="/A001101/b001101.txt">Table of n, a(n) for n=1..1000</a>

%H Amin Witno, <a href="http://www.ijopcm.org/Vol/10/IJOPCM(vol.3.2.3.J.10).pdf">Numbers which factor as their digital sum times a prime</a>, International Journal of Open Problems in Computer Science and Mathematics 3:2 (2010), pp. 132-136.

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

%o import Data.List (findIndices)

%o a001101 n = a001101_list !! (n-1)

%o a001101_list = map succ \$ findIndices p [1..] where

%o p n = m == 0 && a010051 n' == 1 where

%o (n', m) = divMod n (a007953 n)

%o -- _Reinhard Zumkeller_, Jun 16 2011

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

%K nonn,base,nice,changed

%O 1,1

%A Bill Moran (moran1(AT)llnl.gov)

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