cp's OEIS Frontend

A327862 Numbers whose arithmetic derivative is of the form 4k+2, cf. A003415.

%I A327862 #29 Feb 06 2024 16:23:43
%S A327862 9,21,25,33,49,57,65,69,77,85,93,121,129,133,135,141,145,161,169,177,
%T A327862 185,201,205,209,213,217,221,237,249,253,265,289,301,305,309,315,321,
%U A327862 329,341,351,361,365,375,377,381,393,413,417,437,445,453,459,469,473,481,485,489,493,495,497,501,505,517,529,533,537
%N A327862 Numbers whose arithmetic derivative is of the form 4k+2, cf. A003415.
%C A327862 All terms are odd because the terms A068719 are either multiples of 4 or odd numbers.
%C A327862 Odd numbers k for which A064989(k) is one of the terms of A358762. - _Antti Karttunen_, Nov 30 2022
%C A327862 The second arithmetic derivative (A068346) of these numbers is odd. See A235991. - _Antti Karttunen_, Feb 06 2024
%H A327862 Antti Karttunen, <a href="/A327862/b327862.txt">Table of n, a(n) for n = 1..10000</a>
%o A327862 (PARI)
%o A327862 A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
%o A327862 isA327862(n) = (2==(A003415(n)%4));
%o A327862 k=1; n=0; while(k<105, if(isA327862(n), print1(n, ", "); k++); n++);
%Y A327862 Setwise difference A235992 \ A327864.
%Y A327862 Setwise difference A046337 \ A360110.
%Y A327862 Union of A369661 (k' has an even number of prime factors) and A369662 (k' has an odd number of prime factors).
%Y A327862 Subsequences: A001248 (from its second term onward), A108181, A327978, A366890 (when sorted into ascending order), A368696, A368697.
%Y A327862 Cf. A003415, A064989, A068346, A068719, A327863, A327865, A353495 (characteristic function).
%Y A327862 Cf. also A235991, A358762, A358772, A358774.
%K A327862 nonn
%O A327862 1,1
%A A327862 _Antti Karttunen_, Sep 30 2019