cp's OEIS Frontend

A369639 Numbers k, not squarefree, such that the maximal digit in the primorial base representation of k' is <= 3, where k' stands for the arithmetic derivative of k, A003415.

%I A369639 #11 Feb 02 2024 16:12:32
%S A369639 4,8,9,12,16,18,24,25,28,32,36,40,44,45,48,49,50,54,56,60,63,68,76,81,
%T A369639 92,96,98,99,108,112,120,121,125,136,147,153,156,160,175,184,189,192,
%U A369639 196,198,204,208,212,220,225,228,234,236,244,250,252,268,270,280,284,289,296,300,315,316,328,333,338,340,344,361
%N A369639 Numbers k, not squarefree, such that the maximal digit in the primorial base representation of k' is <= 3, where k' stands for the arithmetic derivative of k, A003415.
%C A369639 Nonsquarefree numbers k (A013929) such that A327859(k) = A276086(A003415(k)) is biquadratefree number (A046100), or equally that A328114(A003415(k)) <= 3.
%H A369639 Antti Karttunen, <a href="/A369639/b369639.txt">Table of n, a(n) for n = 1..20000</a>
%H A369639 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A369639 (PARI)
%o A369639 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A369639 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 A369639 isA369639(n) = (n>0 && !issquarefree(n) && ismaxprimobasedigit_at_most(A003415(n),3));
%Y A369639 Cf. A003415, A013929, A046100, A327859, A328114.
%Y A369639 Nonsquarefree terms of A369642 form a subsequence.
%K A369639 nonn
%O A369639 1,1
%A A369639 _Antti Karttunen_, Feb 01 2024