cp's OEIS Frontend

A353485 Numbers k such that no x with an odd arithmetic derivative is encountered when repeatedly prime shifting from k down to 1 with the map x -> A064989(x).

%I A353485 #16 Apr 23 2022 18:12:25
%S A353485 1,4,8,9,16,25,32,36,49,64,72,81,100,108,121,128,144,169,196,200,216,
%T A353485 225,256,288,289,324,361,392,400,432,441,484,512,529,576,625,648,676,
%U A353485 729,784,800,841,864,900,961,968,972,1024,1089,1152,1156,1225,1296,1352,1369,1444,1521,1568,1600,1681,1728,1764,1800,1849
%N A353485 Numbers k such that no x with an odd arithmetic derivative is encountered when repeatedly prime shifting from k down to 1 with the map x -> A064989(x).
%C A353485 Note that k itself must also be in A235992 to be included here. All terms must be powerful (in A001694) because otherwise at some point in the shifting process a number of the form 4u+2 would be encountered, and they are all in A235991.
%H A353485 Antti Karttunen, <a href="/A353485/b353485.txt">Table of n, a(n) for n = 1..10000</a>
%o A353485 (PARI)
%o A353485 A000265(n) = (n>>valuation(n,2));
%o A353485 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A353485 A064989(n) = { my(f=factor(A000265(n))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
%o A353485 isA353485(n) = { while(n>1, if(A003415(n)%2, return(0)); n = A064989(n)); (1); };
%Y A353485 Positions of zeros in A353484.
%Y A353485 Cf. A000290 (subsequence), A003415, A064989, A165560, A235991, A235992.
%Y A353485 Subsequence of A001694.
%K A353485 nonn
%O A353485 1,2
%A A353485 _Antti Karttunen_, Apr 23 2022