OFFSET
1,7
FORMULA
EXAMPLE
a(5) = 1 = card{9/2}.
a(7) = 2 = card{9/2, 27/4}.
a(8) = 3 = card{9/2, 27/4, 15/2}.
a(11) = 5 = card{9/2, 27/4, 15/2, 81/8, 21/2}.
a(12) = 6 = card{9/2, 27/4, 15/2, 81/8, 21/2, 45/4}.
a(13) = 7 = card{9/2, 27/4, 15/2, 81/8, 21/2, 45/4, 25/2}.
a(16) = 9 = card{9/2, 27/4, 15/2, 81/8, 21/2, 45/4, 25/2, 243/16, 63/4}.
It appears that Pi*x_n - n/2 + sqrt(n)/2 ~ A002410(n), where x_n is the n-th term of the above vector.
The numerators of the above vector elements are A374074(n).
The denominators of the above vector elements are 2^(bigomega(A374074(n)) - 1).
MATHEMATICA
z = 100;
k[n_] := Max[1, Floor[Log[3/2, n/2]]];
m[n_] := n 2^(k[n] - 1);
PrimePiK = Table[0, Floor[Log[2, m[z]]], m[z]];
For[i = 2, i <= m[z], i++, PrimePiK[[PrimeOmega[i], i]] = 1]
PrimePiK = Accumulate /@ PrimePiK;
a = Table[PrimePiK[[k[n], m[n]]] - PrimePi[n], {n, z}] (*sequence*)
x = Union@Select[Table[i/2^(PrimeOmega[i] - 1), {i, 1, m[z], 2}], # <= z && Mod[#, 1] != 0 &] (*set*)
PROG
(PARI) nap(n, k) = sum(i=1, n, bigomega(i)==k);
a(n) = my(k=max(1, floor(log(n/2)/(log(3)-log(2))))); nap(n*2^(k-1), k) - primepi(n); \\ Michel Marcus, Jun 27 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Friedjof Tellkamp, Jun 25 2024
STATUS
approved