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%I #13 Feb 02 2022 15:09:15
%S 0,3,11,52,291,1681,11506,89347
%N Number of integers between the n-th and the (n+1)-th primorial such that the maximal exponent in their prime factorization is larger than the maximal digit in their primorial base expansion.
%C a(n) is the number of terms of A350075 in range A002110(n) .. A002110(1+n)-1.
%C The ratio a(n) / A061720(n) develops as:
%C n = 1: 0 / 4 = 0
%C 2: 3 / 24 = 0.125
%C 3: 11 / 180 = 0.061111...
%C 4: 52 / 2100 = 0.247619...
%C 5: 291 / 27720 = 0.010498...
%C 6: 1681 / 480480 = 0.003499...
%C 7: 11506 / 9189180 = 0.001252...
%C 8: 89347 / 213393180 = 0.000419...
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F a(n) = Sum_{k=A002110(n) .. A002110(1+n)-1} [A328114(k) < A051903(k)], where [ ] is the Iverson bracket.
%F For all n, a(n) < A351069(n).
%e Between A002110(2) = 6 and A002110(3) = 30, there are exactly three numbers that satisfy the condition: 8, 9, 16, therefore a(2) = 3.
%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 isA350075(n) = (A051903(A276086(n)) < A051903(n));
%o A351067(n) = sum(k=A002110(n),A002110(1+n)-1,isA350075(k));
%Y Cf. A002110, A051903, A276086, A328114, A350075, A351068 (partial sums), A351069.
%Y Cf. also A327969.
%K nonn,more
%O 1,2
%A _Antti Karttunen_, Feb 02 2022
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