%I #11 Feb 02 2022 15:09:02

%S 3,6,29,122,633,3587,24091,184924

%N Number of integers in range A002110(n) .. A002110(1+n)-1 such that the maximal digit in their primorial base expansion is not larger than the maximal exponent in their prime factorization, where A002110(n) gives the n-th primorial.

%C a(n) is the number of terms of A351038 (numbers k satisfying A328114(k) <= A051903(k)) in range A002110(n) .. A002110(1+n)-1.

%F a(n) = Sum_{k=A002110(n) .. A002110(1+n)-1} A351039(k).

%F For all n, a(n) > A351067(n).

%e There are six numbers in range A002110(2) .. A002110(3)-1 [in 6 .. (30-1)] that satisfy the condition: 6, 7, 8, 9, 12, 16, therefore a(2) = 6.

%o (PARI)

%o A002110(n) = prod(i=1,n,prime(i));

%o A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A351039(n) = (A051903(A276086(n)) <= A051903(n));

%o A351069(n) = sum(k=A002110(n),A002110(1+n)-1,A351039(k));

%Y Cf. A002110, A051903, A276086, A328114, A351038, A351039, A351067, A351070 (partial sums).

%Y Cf. also A327969.

%K nonn,more

%O 1,1

%A _Antti Karttunen_, Feb 02 2022