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

%I A249370 #12 Jan 31 2025 04:27:49
%S A249370 3,5,7,11,12,13,17,19,20,23,27,28,29,31,37,41,43,44,45,47,48,52,53,59,
%T A249370 61,63,67,68,71,73,75,76,79,80,83,89,92,97,99,101,103,107,108,109,112,
%U A249370 113,116,117,124,125,127,131,137,139,147,148,149,151,153,157
%N A249370 Numbers p*m^2, where p is an odd prime and m >= 1, arranged in increasing order.
%p A249370 N:= 1000: # to get all terms <= N
%p A249370 {seq(seq(p*m^2, m = 1 .. floor(sqrt(N/p))), p = select(isprime,[2*i+1 $ i = 1..floor((N-1)/2)]))};
%p A249370 # if using Maple 11 or previous, uncomment the next line
%p A249370 # sort(convert(%,list));
%p A249370 # _Robert Israel_, Oct 30 2014
%t A249370 Take[Sort[Flatten[Table[Prime[n]*m^2, {n, 2, 1000}, {m, 1, 100}]]], 100]
%o A249370 (Python)
%o A249370 from math import isqrt
%o A249370 from sympy import primepi
%o A249370 def A249370(n):
%o A249370     def bisection(f,kmin=0,kmax=1):
%o A249370         while f(kmax) > kmax: kmax <<= 1
%o A249370         kmin = kmax >> 1
%o A249370         while kmax-kmin > 1:
%o A249370             kmid = kmax+kmin>>1
%o A249370             if f(kmid) <= kmid:
%o A249370                 kmax = kmid
%o A249370             else:
%o A249370                 kmin = kmid
%o A249370         return kmax
%o A249370     def f(x): return n+x+(m:=isqrt(x))-sum(((k:=x//y**2)<2)+primepi(k) for y in range(1,m+1))
%o A249370     return bisection(f,n,n) # _Chai Wah Wu_, Jan 30 2025
%Y A249370 Cf. A249369, A229125.
%K A249370 nonn,easy
%O A249370 1,1
%A A249370 _Clark Kimberling_, Oct 26 2014