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%I #15 Jan 05 2023 16:12:52
%S 4,8,12,15,16,20,24,26,27,28,32,35,36,39,40,44,45,48,50,51,52,54,55,
%T 56,60,63,64,68,69,72,74,75,76,80,81,84,86,87,88,90,91,92,95,96,99,
%U 100,102,104,106,108,110,111,112,115,116,117,119,120,122,123,124,125,128,132
%N Numbers n whose k-th arithmetic derivative is nonzero for all k. Complement of A099308.
%C Numbers of the form n = m*p^p (where p is prime), i.e., multiples of some term in A051674, have n' = (m + m')*p^p, which is again of the same form, but strictly larger iff m > 1. Therefore successive derivatives grow to infinity in this case, and they are constant when m = 1. There are other terms in this sequence, but I conjecture that they all eventually lead to a term of this form, e.g., 26 -> 15 -> 8 etc. - _M. F. Hasler_, Apr 09 2015
%D See A003415.
%H T. D. Noe, <a href="/A099309/b099309.txt">Table of n, a(n) for n = 1..10000</a>
%o (PARI) is(n)=until(4>n=factorback(n~)*sum(i=1,#n,n[2,i]/n[1,i]), for(i=1,#n=factor(n)~,n[1,i]>n[2,i]||return(1))) \\ _M. F. Hasler_, Apr 09 2015
%Y Cf. A003415 (arithmetic derivative of n), A099307 (least k such that the k-th arithmetic derivative of n is zero), A099308 (numbers whose k-th arithmetic derivative is zero for some k).
%Y Cf. A341999 (characteristic function),
%Y Positions of zeros in A256750, A351078, A351079 (after their initial zeros), also in A328308, A328312.
%Y Subsequences include: A100716, A327929, A327934, A328251, A359547 (intersection with A048103).
%K nonn
%O 1,1
%A _T. D. Noe_, Oct 12 2004
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