cp's OEIS Frontend

A369664 Numbers k of the form 4m+1, whose arithmetic derivative k' is of the form 4u+2, and k' has an odd number of prime factors.

%I A369664 #9 Feb 06 2024 16:24:22
%S A369664 65,77,141,161,185,201,209,221,301,305,321,341,365,377,381,413,437,
%T A369664 453,481,485,497,501,537,545,589,649,681,689,717,721,729,737,745,749,
%U A369664 785,789,849,893,901,905,917,921,989,1037,1073,1081,1101,1121,1133,1141,1157,1165,1169,1189,1205,1253,1261,1293,1313,1317
%N A369664 Numbers k of the form 4m+1, whose arithmetic derivative k' is of the form 4u+2, and k' has an odd number of prime factors.
%H A369664 Antti Karttunen, <a href="/A369664/b369664.txt">Table of n, a(n) for n = 1..10000</a>
%o A369664 (PARI)
%o A369664 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A369664 isA369664(n) = if(1!=(n%4), 0, my(d=A003415(n)); (2==(d%4) && (bigomega(d)%2)));
%Y A369664 Intersection of A016813 and A369662.
%Y A369664 Subsequence of A369666.
%Y A369664 Cf. A003415, A351228.
%K A369664 nonn
%O A369664 1,1
%A A369664 _Antti Karttunen_, Feb 06 2024