cp's OEIS Frontend

A373479 Numbers k such that A001414(k) and A003415(k) are both multiples of 3, but A083345(k) is not, where A001414 is the sum of prime factors with repetition, A003415 is the arithmetic derivative, and A083345(n) = A003415(n)/gcd(n,A003415(n)).

%I A373479 #10 Jun 07 2024 17:36:39
%S A373479 9,27,72,81,126,180,216,234,243,315,342,378,396,450,540,558,576,585,
%T A373479 612,648,666,693,702,729,774,828,855,945,990,1008,1026,1044,1071,1098,
%U A373479 1125,1134,1188,1206,1287,1314,1350,1395,1422,1440,1449,1476,1530,1620,1665,1674,1692,1728,1746,1755,1764,1827,1836,1854
%N A373479 Numbers k such that A001414(k) and A003415(k) are both multiples of 3, but A083345(k) is not, where A001414 is the sum of prime factors with repetition, A003415 is the arithmetic derivative, and A083345(n) = A003415(n)/gcd(n,A003415(n)).
%C A373479 All terms are multiples of 9.
%C A373479 Not equal to 9*A289142, nor (after the initial term 9), equal to 3*A102217, although most of the terms are.
%H A373479 Antti Karttunen, <a href="/A373479/b373479.txt">Table of n, a(n) for n = 1..20000</a>
%o A373479 (PARI)
%o A373479 A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
%o A373479 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A373479 A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
%o A373479 isA373479(n) = (!(A001414(n)%3) && !(A003415(n)%3) && (A083345(n)%3));
%Y A373479 Setwise difference A373478 \ A373475.
%Y A373479 Subsequence of A008591.
%Y A373479 Cf. A001414, A003415, A083345, A102217, A289142.
%K A373479 nonn
%O A373479 1,1
%A A373479 _Antti Karttunen_, Jun 07 2024