A380404 Number of prime powers that do not exceed the primorial number A002110(n).
0, 1, 4, 16, 60, 377, 3323, 42518, 646580, 12285485, 300378113, 8028681592, 259488951722, 9414917934636, 362597756958862, 15397728568256861, 742238179325555125, 40068968503380861518, 2251262473065725514585, 139566579946046888545036
Offset: 0
Examples
Let P = A002110 and let s = A246655.
a(0) = 0 since P(0) = 1, and the smallest term in s is 2.
a(1) = 1 since P(1) = 2.
a(2) = 4 since P(2) = 6 and the terms in s that do not exceed 6 are {2, 3, 4, 5}.
a(3) = 16 since P(3) = 30; the numbers 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, and 29 are less than 30, etc.
Programs
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Mathematica
Table[Sum[PrimePi[Floor[#^(1/k)]], {k, Floor@ Log2[#]}] &[Product[Prime[i], {i, n}]], {n, 0, 14}]