%I #8 Jan 15 2024 10:05:31
%S 1,158,160,208,212,275,329,374,410,428,473,482,515,533,629,698,700,
%T 707,713,785,910,914,952,1055,1058,1067,1072,1076,1078,1080,1183,1204,
%U 1238,1346,1404,1431,1445,1454,1490,1562,1661,1691,1724,1813,1841,1865,1888,1937,1994,2102,2219,2291,2320,2372,2426,2432,2570
%N Numbers k for which k' / gcd(k,k') is a multiple of 27, where k' stands for the arithmetic derivative of k, A003415(k).
%C Question: What is the asymptotic density of these terms? 0.0253...?
%o (PARI)
%o A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
%o isA369007(n) = !(A083345(n)%27);
%Y Positions of multiples of 27 in A083345.
%Y Subsequence of A369003.
%Y Cf. A003415.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jan 14 2024
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