A376690 -id:A376690 - cp's OEIS frontend

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

David James Sycamore, Oct 13 2024

nonn

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).

			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).

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

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

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 *)

More terms from Michael De Vlieger, Oct 13 2024

cp's OEIS Frontend

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

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