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A189560 Least odd number k such that x' = k has n solutions, where x' is the arithmetic derivative (A003415) of x.

%I A189560 #21 Sep 13 2022 02:20:41
%S A189560 3,5,21,75,151,371,671,791,311,551,1271,1391,1031,2471,2231,4271,1991,
%T A189560 3191,5351,7871,7751,7031,8951,8711,11831,5591,19631,10391,15791,
%U A189560 20711,30071,17111,30551,27191,40031,31391,52631,49271,35591,42311,50951,92231
%N A189560 Least odd number k such that x' = k has n solutions, where x' is the arithmetic derivative (A003415) of x.
%C A189560 See A189559 for k restricted to prime numbers and A189558 for no restrictions on k.
%D A189560 See A003415.
%H A189560 Donovan Johnson, <a href="/A189560/b189560.txt">Table of n, a(n) for n = 0..200</a>
%F A189560 a(n) is the least odd k such that A099302(k) = n.
%o A189560 (Python)
%o A189560 from itertools import count
%o A189560 from sympy import factorint
%o A189560 def A189560(n):
%o A189560     if n == 0:
%o A189560         return 3
%o A189560     mdict = {}
%o A189560     for k in count(1,2):
%o A189560         c = 0
%o A189560         for m in range(1,(k**2>>2)+1):
%o A189560             if m not in mdict:
%o A189560                 mdict[m] = sum((m*e//p for p,e in factorint(m).items()))
%o A189560             if mdict[m] == k:
%o A189560                 c += 1
%o A189560             if c > n:
%o A189560                 break
%o A189560         if c == n:
%o A189560             return k # _Chai Wah Wu_, Sep 12 2022
%Y A189560 Cf. A003415, A189558, A189559.
%K A189560 nonn
%O A189560 0,1
%A A189560 _T. D. Noe_, Apr 24 2011