cp's OEIS Frontend

A384210 Number of numbers <= n of the form p * m^2, where p is a prime and m is an integer >= 1.

%I A384210 #16 Jun 06 2025 14:48:06
%S A384210 0,1,2,2,3,3,4,5,5,5,6,7,8,8,8,8,9,10,11,12,12,12,13,13,13,13,14,15,
%T A384210 16,16,17,18,18,18,18,18,19,19,19,19,20,20,21,22,23,23,24,25,25,26,26,
%U A384210 27,28,28,28,28,28,28,29,29,30,30,31,31,31,31,32,33,33,33,34,35,36,36,37
%N A384210 Number of numbers <= n of the form p * m^2, where p is a prime and m is an integer >= 1.
%C A384210 Partial sums of A358769.
%C A384210 First differs from A055038 at a(30).
%C A384210 a(A229125(n)) = n.
%H A384210 Ridouane Oudra, <a href="/A384210/b384210.txt">Table of n, a(n) for n = 1..10000</a>
%F A384210 a(n) = Sum_{i=1..n} A358769(i).
%F A384210 a(n) = Sum_{i=1..floor(sqrt(n))} pi(floor(n/i^2)), where pi = A000720.
%F A384210 a(n) = - Sum_{i=1..n} lambda(i)*omega(i)*floor(n/i), where lambda = A008836 and omega = A001221.
%p A384210 with(numtheory): A358769:=n-> add(nops(factorset(d)), d in divisors(n)) mod 2:
%p A384210 seq(add(A358769(i), i=1..n), n=1..100);
%o A384210 (PARI) a(n) = sum(k=1, n, isprime(core(k))); \\ _Michel Marcus_, May 29 2025
%o A384210 (Python)
%o A384210 from math import isqrt
%o A384210 from sympy import primepi
%o A384210 def A384210(n): return sum(primepi(n//y**2) for y in range(1,isqrt(n)+1)) # _Chai Wah Wu_, Jun 06 2025
%Y A384210 Cf. A229125, A358769, A000720, A008836, A001221.
%K A384210 nonn
%O A384210 1,3
%A A384210 _Ridouane Oudra_, May 22 2025