cp's OEIS Frontend

A351099 Composite numbers k such that the maximal digit value in primorial base expansion of the arithmetic derivative of k is not larger than the maximal exponent in the prime factorization of k.

%I A351099 #4 Feb 04 2022 16:31:41
%S A351099 4,8,9,10,12,14,15,16,24,25,28,30,32,36,40,45,48,49,50,54,56,58,62,64,
%T A351099 68,74,81,87,96,98,99,108,112,120,125,128,136,155,156,160,161,162,184,
%U A351099 189,192,196,198,203,204,208,209,210,212,217,220,221,224,225,236,244,246,247,250,252,256,268,270,272,280,282,288
%N A351099 Composite numbers k such that the maximal digit value in primorial base expansion of the arithmetic derivative of k is not larger than the maximal exponent in the prime factorization of k.
%C A351099 Composite k such that A328390(k) <= A051903(k).
%C A351099 Composite k for which A051903(A327859(n)) <= A051903(k).
%o A351099 (PARI)
%o A351099 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A351099 A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
%o A351099 A328114(n) = { my(s=0, p=2); while(n, s = max(s, (n%p)); n = n\p; p = nextprime(1+p)); (s); };
%o A351099 isA351099(n) = (n>1&&!isprime(n)&&(A328114(A003415(n)) <= A051903(n)));
%Y A351099 Cf. A003415, A051903, A276086, A327859, A328390, A351097, A351098 (subsequence).
%K A351099 nonn
%O A351099 1,1
%A A351099 _Antti Karttunen_, Feb 03 2022