The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A303704 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A303704

Numbers k such that all coprime quadratic residues modulo k are squares.
(history; published version)

#26 by N. J. A. Sloane at Sun Feb 17 20:47:35 EST 2019

STATUS

proposed

approved

#25 by Jianing Song at Sun Feb 17 00:11:50 EST 2019

STATUS

editing

proposed

Discussion

Sun Feb 17

02:47

Jianing Song: I wonder: sqrt or sqrtint, both are ok is this case, which should be faster ?

#24 by Jianing Song at Sun Feb 17 00:11:21 EST 2019

PROG

(PARI) for(k=1, 130729, if(eulerphi(k)/2^#znstar(k)[2] <= floor(sqrt(k)), , for(j=1, k, if(gcd(j, k)==1&&!issquare(j^2%k), break()); if(j==k, print1(k, ", "))))) \\ Jianing Song, Feb 15 2019

STATUS

proposed

editing

Discussion

Sun Feb 17

00:11

Jianing Song: Sorry.

#23 by Jianing Song at Sun Feb 17 00:08:00 EST 2019

STATUS

editing

proposed

#22 by Jianing Song at Sun Feb 17 00:07:53 EST 2019

PROG

(PARI) for(k=1, 130729, if(eulerphi(k)/2^#znstar(k)[2] <= floor(sqrt(k), ), for(j=1, k, if(gcd(j, k)==1&&!issquare(j^2%k), break()); if(j==k, print1(k, ", "))))) \\ Jianing Song, Feb 15 2019

STATUS

proposed

editing

#21 by Jianing Song at Sat Feb 16 23:58:09 EST 2019

STATUS

editing

proposed

Discussion

Sun Feb 17

00:02

Jianing Song: Sorry, about 1 sec

#20 by Jianing Song at Sat Feb 16 23:57:24 EST 2019

PROG

(PARI) for(k=1, 130729, if(eulerphi(k)/2^#znstar(k)[2] <= sqrt(k), for(j=1, k, if(gcd(j, k)==1&&!issquare(j^2%k), break()); if(j==k, print1(k, ", ")))) ) \\ Jianing Song, Feb 15 2019

STATUS

proposed

editing

Discussion

Sat Feb 16

23:58

Jianing Song: The program now uses less than 0.8 sec !

#19 by Jianing Song at Fri Feb 15 03:53:14 EST 2019

STATUS

editing

proposed

#18 by Jianing Song at Fri Feb 15 03:52:38 EST 2019

PROG

(PARI) for(k=1, 130729, for(j=1, k, if(gcd(j, k)==1&&!issquare(j^2%k), break()); if(j==k, print1(k, ", ")))) \\ Jianing Song, Feb 15 2019

STATUS

proposed

editing

#17 by Jianing Song at Thu Feb 14 17:50:11 EST 2019

STATUS

editing

proposed

Discussion

Thu Feb 14

17:50

Jianing Song: Sorry, I will check A000625 later