A249370 Numbers p*m^2, where p is an odd prime and m >= 1, arranged in increasing order.

3, 5, 7, 11, 12, 13, 17, 19, 20, 23, 27, 28, 29, 31, 37, 41, 43, 44, 45, 47, 48, 52, 53, 59, 61, 63, 67, 68, 71, 73, 75, 76, 79, 80, 83, 89, 92, 97, 99, 101, 103, 107, 108, 109, 112, 113, 116, 117, 124, 125, 127, 131, 137, 139, 147, 148, 149, 151, 153, 157

Offset: 1

Author

Clark Kimberling, Oct 26 2014

Keywords

• nonn
• easy

Crossrefs

Cf. A249369, A229125.

Programs

Maple

N:= 1000: # to get all terms <= N
{seq(seq(p*m^2, m = 1 .. floor(sqrt(N/p))), p = select(isprime,[2*i+1 $ i = 1..floor((N-1)/2)]))};
# if using Maple 11 or previous, uncomment the next line
# sort(convert(%,list));
# Robert Israel, Oct 30 2014

Mathematica

Take[Sort[Flatten[Table[Prime[n]*m^2, {n, 2, 1000}, {m, 1, 100}]]], 100]

Python

from math import isqrt
from sympy import primepi
def A249370(n):
    def bisection(f,kmin=0,kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        kmin = kmax >> 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    def f(x): return n+x+(m:=isqrt(x))-sum(((k:=x//y**2)<2)+primepi(k) for y in range(1,m+1))
    return bisection(f,n,n) # Chai Wah Wu, Jan 30 2025