cp's OEIS Frontend

A334099 The least k for which A329697(k) = n; Position of first occurrence of n (and also records) in A329697.

%I A334099 #28 May 27 2020 02:11:23
%S A334099 1,3,7,19,43,127,283,659,1319,3957,9227,21599,50123,129263,258527,
%T A334099 775581,1551163,4340087,9750239,27353747,65148847,156067127,340997113,
%U A334099 955523423
%N A334099 The least k for which A329697(k) = n; Position of first occurrence of n (and also records) in A329697.
%C A334099 Note that although most of the terms after 1 are primes, we also have a few composites: a(9) = a(1)*a(8) = 3*1319 = 3957, a(15) = a(1)*a(14) = 3*258527 = 775581, a(22) = a(8)*a(14) = 340997113.
%C A334099 a(n) <= 3^n and in particular, a(n+1) <= 3*a(n), n > 0 and more generally a(n + m) <= a(n) * a(m) where m, n >= 0. - _David A. Corneth_, Apr 15 2020
%C A334099 The above follows because A329697 is totally additive.
%F A334099 For all n >= 0, A329697(a(n)) = n.
%t A334099 With[{s = Array[Length@ NestWhileList[# - #/FactorInteger[#][[-1, 1]] &, #, # != 2^IntegerExponent[#, 2] &] - 1 &, 10^6]}, {1}~Join~Array[FirstPosition[s, #][[1]] &, Max@ s]] (* _Michael De Vlieger_, Apr 30 2020 *)
%o A334099 (PARI)
%o A334099 A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
%o A334099 m=-1; k=0; for(n=1,2^32, t=A329697(n); if(t>m, m=t; write("b334099.txt", k, " ", n); k++));
%Y A334099 The leftmost column of A334100.
%Y A334099 Cf. A329697 (a left inverse).
%Y A334099 Cf. A067513.
%Y A334099 Cf. A007755, A105017, and also A329662 (analogous sequence when using the map k -> k + k/p).
%K A334099 nonn,more
%O A334099 0,2
%A A334099 _Antti Karttunen_, Apr 14 2020