A351069 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.

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

Offset: 1

Author

Antti Karttunen, Feb 02 2022

Keywords

• nonn
• more

Comments

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

Examples

			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.
		

Crossrefs

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

Cf. also A327969.

Programs

PARI

A002110(n) = prod(i=1,n,prime(i));
A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A351039(n) = (A051903(A276086(n)) <= A051903(n));
A351069(n) = sum(k=A002110(n),A002110(1+n)-1,A351039(k));

Formula

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

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