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A096294 Triangle T(n,k) read by rows: for n >=0 and n >= k >=0, the fraction of positive integers with exactly k of the first n primes as divisors is T(n,k)/A002110(n).

%I A096294 #15 Jul 29 2019 13:13:13
%S A096294 1,1,1,2,3,1,8,14,7,1,48,92,56,13,1,480,968,652,186,23,1,5760,12096,
%T A096294 8792,2884,462,35,1,92160,199296,152768,54936,10276,1022,51,1,1658880,
%U A096294 3679488,2949120,1141616,239904,28672,1940,69,1,36495360,82607616
%N A096294 Triangle T(n,k) read by rows: for n >=0 and n >= k >=0, the fraction of positive integers with exactly k of the first n primes as divisors is T(n,k)/A002110(n).
%C A096294 Sum of entries in n-th row is A002110(n), the product of the first n primes (primorial numbers, first definition).
%C A096294 From _Peter Munn_, Apr 10 2017: (Start)
%C A096294 T(n,k) is a count of those integers in any interval of A002110(n) integers that have exactly k of the first n primes as divisors. The count is the same for each such interval because each of the first n primes is a factor of an integer m if and only if it is a factor of m + A002110(n).
%C A096294 A284411(m) is least p=prime(n) such that 2*Sum_{k=0..m-1} T(n,k) < A002110(n).
%C A096294 (End)
%e A096294 Triangle begins:
%e A096294 1
%e A096294 1 1
%e A096294 2 3 1
%e A096294 8 14 7 1
%e A096294 48 92 56 13 1
%e A096294 480 968 652 186 23 1
%o A096294 (PARI) primo(n) = prod(k=1, n, prime(k));
%o A096294 row(n) = {v = vector(n+1); for (k=1, primo(n), f = factor(k)[,1]; v[1+sum(j=1, #f, primepi(f[j])<=n)]++;); v;} \\ _Michel Marcus_, Apr 29 2017
%Y A096294 First column is A005867; second column is A078456. See also A096180.
%Y A096294 Cf. A194156, A284411.
%K A096294 nonn,tabl
%O A096294 0,4
%A A096294 _Matthew Vandermast_, Jun 24 2004