%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