cp's OEIS Frontend

A369662 Numbers k whose arithmetic derivative k' is of the form 4m+2, and k' has an odd number of prime factors.

%I A369662 #11 Feb 06 2024 16:23:38
%S A369662 65,77,135,141,161,185,201,209,221,301,305,315,321,341,351,365,377,
%T A369662 381,413,437,453,481,485,495,497,501,537,545,589,649,681,689,717,721,
%U A369662 729,735,737,745,749,785,789,849,855,893,901,905,917,921,975,989,999,1035,1037,1073,1081,1101,1121,1133,1141,1157,1165
%N A369662 Numbers k whose arithmetic derivative k' is of the form 4m+2, and k' has an odd number of prime factors.
%C A369662 Equally, numbers k whose arithmetic derivative k' is congruent to 2 modulo 4 and A276085(k') is congruent to 1 modulo 4.
%C A369662 A003415((1/2)*A003415(a(n))) is always even.
%H A369662 Antti Karttunen, <a href="/A369662/b369662.txt">Table of n, a(n) for n = 1..10000</a>
%o A369662 (PARI)
%o A369662 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A369662 isA369662(n) = { my(d=A003415(n)); (2==(d%4) && (bigomega(d)%2)); };
%Y A369662 Setwise difference A327862 \ A369661.
%Y A369662 Cf. A003415, A276085.
%Y A369662 Subsequences: A369664 (terms of the form 4m+1).
%K A369662 nonn
%O A369662 1,1
%A A369662 _Antti Karttunen_, Feb 06 2024