The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A354199

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A354199

a(n) = 1 if in the prime factorization of n there is no prime factor of form 4k+1 and any prime factor of form 4k+3 occurs with an even multiplicity, otherwise 0.
(history; published version)

#13 by Michael De Vlieger at Wed May 25 22:51:26 EDT 2022

STATUS

proposed

approved

#12 by Antti Karttunen at Wed May 25 21:39:42 EDT 2022

STATUS

editing

proposed

#11 by Antti Karttunen at Wed May 25 21:32:21 EDT 2022

LINKS

Antti Karttunen, <a href="/A354199/b354199.txt">Table of n, a(n) for n = 1..100000</a>

STATUS

approved

editing

#10 by Michael De Vlieger at Wed May 25 09:14:07 EDT 2022

STATUS

proposed

approved

#9 by Amiram Eldar at Wed May 25 04:51:43 EDT 2022

STATUS

editing

proposed

#8 by Amiram Eldar at Wed May 25 04:51:41 EDT 2022

MATHEMATICA

a[1] = 1; a[n_] := If[AllTrue[FactorInteger[n], First[#] == 2 || (Mod[First[#], 4] == 3 && EvenQ[Last[#]]) &], 1, 0]; Array[a, 100] (* Amiram Eldar, May 25 2022 *)

STATUS

proposed

editing

#7 by Antti Karttunen at Wed May 25 04:39:51 EDT 2022

STATUS

editing

proposed

#6 by Antti Karttunen at Wed May 25 04:13:02 EDT 2022

PROG

(PARI)

A004018(n) = if(n<1, n==0, 4 * sumdiv( n, d, (d%4==1) - (d%4==3))); \\ From A004018

A354199(n) = (4==A004018(n));

#5 by Antti Karttunen at Wed May 25 04:12:22 EDT 2022

FORMULA

a(n) = [A002654(n) == 1] = [A004018(n) == 4], where [ ] is the Iverson bracket.

PROG

(PARI) A354199(n) = (1==sumdiv( n, d, (d%4==1) - (d%4==3)));

CROSSREFS

Cf. A002144, A002145, A002654, A004018, A053866.

#4 by Antti Karttunen at Wed May 25 04:07:07 EDT 2022

PROG

(PARI) A354199(n) = ((issquare(n) || issquare(2*n)) && !A353814(n)); \\ Uses the program given in A353814.

A353814(n) = { my(f = factor(n), nb1 = 0, p, ep); for(i=1, #f~, p = f[i, 1]; ep = f[i, 2]; if(1==(p%4), nb1++, if(3==(p%4) && ep%2, return(0)))); (nb1>0); };

A354199(n) = ((issquare(n) || issquare(2*n)) && !A353814(n));