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A327933 Numbers such that the smallest prime factor of their arithmetic derivative is 3.

%I A327933 #11 Nov 04 2022 14:42:38
%S A327933 14,18,26,27,38,45,50,54,62,63,74,86,90,99,110,117,122,125,126,134,
%T A327933 146,153,158,162,170,171,194,198,206,207,218,230,234,242,243,254,261,
%U A327933 270,275,278,279,290,302,306,314,326,333,342,343,362,369,374,378,386,387,398,405,410,414,422,423,425,446,450,458,470
%N A327933 Numbers such that the smallest prime factor of their arithmetic derivative is 3.
%C A327933 Numbers n for which A086134(n) = 3.
%C A327933 Numbers whose arithmetic derivative is an odd multiple of 3.
%H A327933 Antti Karttunen, <a href="/A327933/b327933.txt">Table of n, a(n) for n = 1..10000</a>
%o A327933 (PARI)
%o A327933 A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
%o A327933 A086134(n) = { my(d=A003415(n)); if(d<=1,0,factor(d)[1, 1]); };
%o A327933 isA327933(n) = (3==A086134(n));
%o A327933 (Python)
%o A327933 from itertools import count, islice
%o A327933 from sympy import factorint
%o A327933 def A327933_gen(startvalue=2): # generator of terms >= startvalue
%o A327933     return filter(lambda n: (m:=sum((n*e//p for p,e in factorint(n).items())))&1 and not m%3, count(max(startvalue,2)))
%o A327933 A327933_list = list(islice(A327933_gen(),40)) # _Chai Wah Wu_, Nov 04 2022
%Y A327933 Cf. A003415, A086134, A235992, A327935.
%Y A327933 Intersection of A235991 and A327863.
%K A327933 nonn
%O A327933 1,1
%A A327933 _Antti Karttunen_, Sep 30 2019