A129253 Number of numbers not greater than n having at least one divisor p^e with p<=e, p prime.

0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 22, 23

Offset

1,8

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(1) = 1, a(n+1) = if A129251(n+1) > 0 then a(n-1)+1 else a(n-1).

a(n) ~ c * n, where c = 1 - Product_{p prime} (1 - 1/p^p) = 0.2780097655... . - Amiram Eldar, Apr 15 2025

Mathematica

Accumulate[Table[Boole[n > 1 && AnyTrue[FactorInteger[n], First[#] <= Last[#] &]], {n, 1, 100}]] (* Amiram Eldar, Apr 15 2025 *)

Crossrefs

Partial sums of A342023.

Cf. A129251.

Sequence in context: A075245 A367329 A328301 * A389975 A008652 A195120

Adjacent sequences: A129250 A129251 A129252 * A129254 A129255 A129256

Keyword

nonn,easy

Author

Reinhard Zumkeller, Apr 07 2007

Status

approved