cp's OEIS Frontend

A341518 Numbers k such that the primorial base representation of their arithmetic derivative does not contain digits larger than 1.

%I A341518 #18 Feb 04 2024 09:03:01
%S A341518 0,1,2,3,5,7,9,10,11,13,14,15,16,17,19,23,28,29,30,31,37,41,43,45,47,
%T A341518 53,58,59,61,62,67,71,73,74,79,83,87,89,97,101,103,107,108,109,112,
%U A341518 113,127,131,136,137,139,149,151,155,157,161,163,167,173,179,181,189,191,193,197,198,199,203,209,210,211,212,217
%N A341518 Numbers k such that the primorial base representation of their arithmetic derivative does not contain digits larger than 1.
%C A341518 Numbers k for which A328390(k) <= 1, numbers k such that A003415(k) is in A276156.
%C A341518 Numbers k such that A327859(k) = A276086(A003415(k)) is squarefree.
%H A341518 Antti Karttunen, <a href="/A341518/b341518.txt">Table of n, a(n) for n = 1..20000</a>
%H A341518 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A341518 For all n > 2, A328390(a(n)) = A328114(A003415(a(n))) = 1.
%o A341518 (PARI)
%o A341518 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A341518 ismaxprimobasedigit_at_most(n,k) = { my(s=0, p=2); while(n, if((n%p)>k, return(0)); n = n\p; p = nextprime(1+p)); (1); };
%o A341518 isA341518(n) = ismaxprimobasedigit_at_most(A003415(n),1); \\ _Antti Karttunen_, Feb 03 2024
%Y A341518 Cf. A003415, A005117, A049345, A276086, A276156, A327859, A328114, A328390.
%Y A341518 Positions of nonzero terms in A341517.
%Y A341518 Subsequences: A000040, A327978, A328232, A369647 (terms k where A051903(k) obtains novel values).
%Y A341518 Cf. also A327969.
%K A341518 nonn
%O A341518 1,3
%A A341518 _Antti Karttunen_, Feb 28 2021