cp's OEIS Frontend

A350075 Numbers whose maximal digit in their primorial base expansion is less than the maximal exponent in their prime factorization.

%I A350075 #20 Feb 02 2022 20:37:38
%S A350075 8,9,16,32,36,40,48,64,72,80,81,96,112,128,212,216,224,240,242,243,
%T A350075 248,250,256,270,272,280,288,304,320,352,384,424,432,448,456,459,464,
%U A350075 480,486,488,496,512,528,544,576,640,648,672,704,720,729,736,768,864,896,928,960,972,1024,1088,1152,1216,1280,1408,1536,2048
%N A350075 Numbers whose maximal digit in their primorial base expansion is less than the maximal exponent in their prime factorization.
%C A350075 Numbers k for which the maximal prime exponent of A276086(k) is less than the maximal prime exponent of k, A051903(k).
%C A350075 Numbers k for which A328114(k) < A051903(k).
%C A350075 Numbers such that when the map x -> A276086(x) is applied to them, the maximal exponent in the prime factorization (A051903) decreases.
%H A350075 Antti Karttunen, <a href="/A350075/b350075.txt">Table of n, a(n) for n = 1..13544; terms less than 9699690</a>
%H A350075 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%e A350075 In primorial base (see A049345) 9 = 3^2 is written as "111" (because 1*6 + 1*2 + 1*1 = 9), whose maximal digit (1) is less than the maximal exponent in the prime factorization of 9 (2), therefore 9 is included in this sequence.
%e A350075 In primorial base 2048 = 2^11 is written as "95110", whose maximal digit 9 is less than 11, therefore 2048 is included in this sequence.
%o A350075 (PARI)
%o A350075 A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
%o A350075 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A350075 isA350075(n) = (A051903(A276086(n)) < A051903(n));
%Y A350075 Cf. A049345, A051903, A276086, A328114, A350076 (complement), A351067 and A351068 (counts).
%Y A350075 Positions of negative terms in A350074.
%Y A350075 Subsequence of A351038.
%Y A350075 Cf. also A351075.
%K A350075 nonn,base
%O A350075 1,1
%A A350075 _Antti Karttunen_, Feb 01 2022