The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A167181 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A167181

Squarefree numbers such that all prime factors are == 3 mod 4.
(history; published version)

#34 by Michel Marcus at Fri Mar 08 08:08:02 EST 2024

STATUS

reviewed

approved

#33 by Joerg Arndt at Fri Mar 08 07:56:07 EST 2024

STATUS

proposed

reviewed

#32 by Amiram Eldar at Fri Mar 08 03:42:25 EST 2024

STATUS

editing

proposed

#31 by Amiram Eldar at Fri Mar 08 03:30:59 EST 2024

FORMULA

The number of terms that do not exceed x is ~ c * x / sqrt(log(x)), where c = A243379/(2*sqrt(A175647)) = 0.4165140462... (Jakimczuk, 2024, Theorem 3.10, p. 26). - _Amiram Eldar_, Mar 08 2024

#30 by Amiram Eldar at Fri Mar 08 03:26:25 EST 2024

CROSSREFS

Cf. A002145, A004613, A004614, A005117, A231754.

#29 by Amiram Eldar at Fri Mar 08 03:25:50 EST 2024

LINKS

Rafael Jakimczuk, <a href="http://dx.doi.org/10.13140/RG.2.2.27745.48487">Generalizations of Mertens's Formula and k-Free and s-Full Numbers with Prime Divisors in Arithmetic Progression</a>, ResearchGate, 2024.

FORMULA

The number of terms that do not exceed x is ~ c * x / sqrt(log(x)), where c = A243379/(2*sqrt(A175647)) = 0.4165140462... (Jakimczuk, 2024, Theorem 3.10, p. 26).

CROSSREFS

Cf. A175647, A243379.

KEYWORD

nonn,easy

STATUS

approved

editing

#28 by N. J. A. Sloane at Sun Apr 16 21:21:47 EDT 2023

NAME

Squarefree numbers such that all prime factors are == 3 (mod 4).

COMMENTS

Numbers k such that x^2 + y^2 is not divisible by k where x and y are both not divisible by k. - Yifan Xie, Apr 16 2023

CROSSREFS

Cf. A002144, A002145, A004613, A004614, A005117.

KEYWORD

nonn,changed

nonn

STATUS

proposed

approved

#27 by Yifan Xie at Sun Apr 16 06:51:48 EDT 2023

STATUS

editing

proposed

Discussion

Sun Apr 16

08:28

Joerg Arndt: This a (bad) rephrasing of the comment *right* above.

08:32

Yifan Xie: These are completely different...

#26 by Yifan Xie at Sun Apr 16 06:50:36 EDT 2023

NAME

Squarefree numbers such that all prime factors are == 3 (mod 4).

COMMENTS

Numbers k such that x^2 + y^2 is not divisible by k where x and y are both not divisible by k. - Yifan Xie, Apr 16 2023

CROSSREFS

Cf. A002144, A002145, A004613, A004614, A005117.

STATUS

approved

editing

Discussion

Sun Apr 16

06:51

Yifan Xie: Possibly needs clarification

#25 by Joerg Arndt at Fri Apr 22 02:37:20 EDT 2016

STATUS

reviewed

approved