A380404 - OEIS

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

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

FORMULA

a(n) = Sum_{k = 1..floor(log_2(P(n)))} pi(floor(P(n)^(1/k))), where P(n) = A002110(n).

a(n) = A000849(n) + A380402(n).

EXAMPLE

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.

MATHEMATICA

Table[Sum[PrimePi[Floor[#^(1/k)]], {k, Floor@ Log2[#]}] &[Product[Prime[i], {i, n}]], {n, 0, 14}]

CROSSREFS

Cf. A000849, A002110, A182908, A246655, A380402.

Sequence in context: A234008 A355351 A203153 * A382640 A126929 A338531

Adjacent sequences: A380401 A380402 A380403 * A380405 A380406 A380407

KEYWORD

nonn,hard,more

AUTHOR

Michael De Vlieger, Jan 24 2025

STATUS

approved