A377028 a(n) = number of integers k <= n such that k is a term in A055932.

1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17

Offset

1,2

Comments

Sequence counts the number of k <= n such that the squarefree kernel of k = rad(k) = A007947(k) is a primorial number (a term in A002110). Similar counting function to A000720 (number of primes <= n).

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

a(30) = 10 because there are 10 numbers k <= 30 which are terms in A005932 (namely : 1,2,4,6,8,12,16,18,24,30).

Mathematica

c = 0; fQ[x_] := Or[IntegerQ@ Log2[x], And[EvenQ[x], Union@ Differences@ PrimePi[FactorInteger[x][[All, 1]] ] == {1}] ]; Reap[Do[If[fQ[n], c++]; Sow[c], {n, 10^4}] ][[-1, 1]] (* Michael De Vlieger, Oct 13 2024 *)

Crossrefs

Cf. A000720, A002110, A007947, A055932, A376690.

Sequence in context: A228720 A219652 A069924 * A225559 A082479 A090616

Adjacent sequences: A377025 A377026 A377027 * A377029 A377030 A377031

Keyword

nonn

Author

David James Sycamore, Oct 13 2024

Extensions

More terms from Michael De Vlieger, Oct 13 2024

Status

approved