cp's OEIS Frontend

A351098 Numbers k such that the maximal digit value in primorial base expansion of the arithmetic derivative of k is less than the maximal exponent in the prime factorization of k.

%I A351098 #17 Feb 02 2024 09:06:33
%S A351098 8,9,16,24,28,32,40,45,48,81,96,108,112,120,125,128,136,160,184,189,
%T A351098 192,198,208,212,225,236,244,250,256,270,288,296,352,361,459,507,625,
%U A351098 640,768,800,832,864,896,928,960,972,1008,1024,1056,1088,1104,1120,1152,1168,1184,1232,1272,1280,1320,1344,1350,1408,1440
%N A351098 Numbers k such that the maximal digit value in primorial base expansion of the arithmetic derivative of k is less than the maximal exponent in the prime factorization of k.
%C A351098 Numbers k such that A328390(k) < A051903(k).
%C A351098 Numbers k for which A051903(A327859(n)) < A051903(k).
%C A351098 These seem to be rarer than A351075. All terms are nonsquarefree.
%H A351098 Antti Karttunen, <a href="/A351098/b351098.txt">Table of n, a(n) for n = 1..20000</a>
%H A351098 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A351098 (PARI)
%o A351098 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A351098 A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
%o A351098 A328114(n) = { my(s=0, p=2); while(n, s = max(s, (n%p)); n = n\p; p = nextprime(1+p)); (s); };
%o A351098 isA351098(n) = (A328114(A003415(n)) < A051903(n));
%o A351098 (PARI) \\ Or see A369637.
%Y A351098 Positions of negative terms in A351097. Subsequence of A013929 and of A351099.
%Y A351098 Cf. A003415, A051903, A276086, A327859, A328390, A369637 (characteristic function).
%Y A351098 Cf. also A351075.
%K A351098 nonn
%O A351098 1,1
%A A351098 _Antti Karttunen_, Feb 03 2022