A351069 - OEIS

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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.

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

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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.

LINKS

Table of n, a(n) for n=1..8.

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

Cf. also A327969.

Sequence in context: A007228 A326074 A096155 * A369607 A007452 A046981

Adjacent sequences: A351066 A351067 A351068 * A351070 A351071 A351072

KEYWORD

nonn,more

AUTHOR

Antti Karttunen, Feb 02 2022

STATUS

approved