A327935 - OEIS

%I #10 Nov 04 2022 14:42:43

%S 6,46,75,106,150,166,175,226,250,266,325,346,350,406,429,466,475,526,

%T 546,550,586,646,650,682,706,750,759,766,775,826,847,850,886,925,950,

%U 966,1006,1050,1075,1083,1106,1126,1150,1186,1209,1246,1250,1254,1306,1326,1342,1366,1406,1419,1421,1450,1486,1525,1526,1546

%N Numbers for which the smallest prime factor of their arithmetic derivative is 5.

%C Numbers n for which A086134(n) = 5.

%C Numbers whose arithmetic derivative is an odd multiple of five, but is not a multiple of three.

%H Antti Karttunen, <a href="/A327935/b327935.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI)

%o 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 A086134(n) = { my(d=A003415(n)); if(d<=1,0,factor(d)[1, 1]); };

%o isA327935(n) = (5==A086134(n));

%o (Python)

%o from itertools import count, islice

%o from sympy import factorint

%o def A327935_gen(startvalue=2): # generator of terms  >= startvalue

%o     return filter(lambda n: (m:=sum((n*e//p for p,e in factorint(n).items())))&1 and m%3 and not m%5, count(max(startvalue,2)))

%o A327935_list = list(islice(A327935_gen(),40)) # _Chai Wah Wu_, Nov 04 2022

%Y Cf. A003415, A086134, A235992, A327933.

%Y Subsequence of A235991, and also of A327865.

%K nonn

%O 1,1

%A _Antti Karttunen_, Sep 30 2019