cp's OEIS Frontend

A369007 Numbers k for which k' / gcd(k,k') is a multiple of 27, where k' stands for the arithmetic derivative of k, A003415(k).

%I A369007 #15 Nov 12 2024 16:00:30
%S A369007 1,158,160,208,212,275,329,374,410,428,473,482,515,533,629,698,700,
%T A369007 707,713,785,910,914,952,1055,1058,1067,1072,1076,1078,1080,1183,1204,
%U A369007 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 A369007 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 A369007 Question: What is the asymptotic density of these terms? 0.0253...?
%C A369007 A multiplicative semigroup: if m and n are in the sequence, then so is m*n. - _Antti Karttunen_, Nov 11 2024
%H A369007 Antti Karttunen, <a href="/A369007/b369007.txt">Table of n, a(n) for n = 1..20000</a>
%F A369007 For all n >= 1, A007949(a(n)) = 3*k, for k >= 0. - _Antti Karttunen_, Nov 12 2024
%o A369007 (PARI)
%o A369007 A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
%o A369007 isA369007(n) = !(A083345(n)%27);
%Y A369007 Positions of multiples of 27 in A083345.
%Y A369007 Subsequence of A369003 and of A369644.
%Y A369007 Cf. A003415, A007949.
%Y A369007 Cf. also A377872.
%K A369007 nonn
%O A369007 1,2
%A A369007 _Antti Karttunen_, Jan 14 2024