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A327864 Numbers whose arithmetic derivative is a multiple of 4, cf. A003415.

%I A327864 #13 Feb 02 2023 15:06:25
%S A327864 0,1,4,8,12,15,16,20,24,28,32,35,36,39,40,44,48,51,52,55,56,60,64,68,
%T A327864 72,76,80,81,84,87,88,91,92,95,96,100,104,108,111,112,115,116,119,120,
%U A327864 123,124,128,132,136,140,143,144,148,152,155,156,159,160,164,168,172,176,180,183,184,187,188,189,192,196,200,203
%N A327864 Numbers whose arithmetic derivative is a multiple of 4, cf. A003415.
%C A327864 Also k such that A359423(k) is a multiple of 4. - _Antti Karttunen_, Jan 02 2023
%C A327864 A multiplicative semigroup; if m and n are in the sequence then so is m*n. - _Antti Karttunen_, Feb 01 2023
%H A327864 Antti Karttunen, <a href="/A327864/b327864.txt">Table of n, a(n) for n = 1..10000</a>
%F A327864 {k | A353493(k)=0}. - _Antti Karttunen_, Jan 02 2023
%o A327864 (PARI)
%o A327864 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 A327864 isA327864(n) = !(A003415(n)%4);
%o A327864 k=1; n=0; while(k<105, if(isA327864(n), print1(n, ", "); k++); n++);
%Y A327864 Subsequence of A235992.
%Y A327864 Union of A008586 and A360110.
%Y A327864 Cf. A003415, A327862, A327863, A327865, A353493, A353494 (characteristic function), A359423.
%K A327864 nonn
%O A327864 1,3
%A A327864 _Antti Karttunen_, Sep 30 2019