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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.
6
3, 6, 29, 122, 633, 3587, 24091, 184924
OFFSET
1,1
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.
FORMULA
a(n) = Sum_{k=A002110(n) .. A002110(1+n)-1} A351039(k).
For all n, a(n) > A351067(n).
EXAMPLE
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.
PROG
(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));
CROSSREFS
Cf. also A327969.
Sequence in context: A007228 A326074 A096155 * A369607 A007452 A046981
KEYWORD
nonn,more
AUTHOR
Antti Karttunen, Feb 02 2022
STATUS
approved