A071821 -id:A071821 - cp's OEIS frontend

A071824 Number of integers <= n whose largest prime factor is of the form 4*k+1.

0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 7, 8, 8, 8, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 13, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 18, 19, 20, 20, 20, 20, 20, 21, 21, 22, 23, 23, 23, 23, 24, 24, 24, 25, 25, 25, 25, 25, 26, 27, 28, 28, 28, 29, 29

Offset: 1

Benoit Cloitre, Jun 07 2002

Conjecture : for n > 1000 a(n) - n/2 < - sqrt(n) ( if b(n) denotes the number of x with largest prime factor of the form 4k+3 less than or equal to n, it is conjectured that if n > 1000 b(n)- n/2 > sqrt(n) )

Partial sums of the indicator function of A071821. - Robert Israel, Nov 05 2024

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A071821.

filter:= n -> max(numtheory:-factorset(n)) mod 4 = 1:
R:= NULL: t:= 0:
for i from 1 to 100 do
  if filter(i) then t:= t+1 fi;
  R:= R,t
od:
R; # Robert Israel, Nov 05 2024

Join[{0}, Accumulate[Boole[Divisible[FactorInteger[Range[2, 100]][[All, -1, 1]] - 1, 4]]]] (* Paolo Xausa, Nov 23 2024 *)

a(n)=sum(i=2, n, ((factor(i)[omega(i),1])-1)%4==0)

from sympy import factorint
a = lambda n: sum(1 for i in range(2, n + 2) if (max(factorint(i).keys()) - 1) & 3 == 0)
print([a(n) for n in range(0, 79)]) # Darío Clavijo, Nov 05 2024

Missing a(1)=0 inserted by Sean A. Irvine, Aug 15 2024

Name edited by Michel Marcus, Nov 05 2024

A071822 Numbers whose largest prime factor is of the form 4k+3.

Original entry on oeis.org

3, 6, 7, 9, 11, 12, 14, 18, 19, 21, 22, 23, 24, 27, 28, 31, 33, 35, 36, 38, 42, 43, 44, 46, 47, 48, 49, 54, 55, 56, 57, 59, 62, 63, 66, 67, 69, 70, 71, 72, 76, 77, 79, 81, 83, 84, 86, 88, 92, 93, 94, 95, 96, 98, 99, 103, 105, 107, 108, 110, 112, 114, 115, 118, 121, 124

Offset: 1

Benoit Cloitre, Jun 07 2002

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A004767, A006530, A071821.

Select[Range[125], Mod[FactorInteger[#][[-1,1]], 4] == 3 &] (* Amiram Eldar, May 04 2022 *)

for(n=2,200,if((component(component(factor(n),1),omega(n))-3)%4==0,print1(n,",")))

Numbers k such that A006530(k) == 3 (mod 4).

cp's OEIS Frontend

A071824 Number of integers <= n whose largest prime factor is of the form 4*k+1.

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