The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A353813 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A353813

a(n) = 1 if n has exactly one prime factor of form 4*k+1 (when counted with multiplicity) and no prime factor 4*k+3 with odd multiplicity, otherwise 0.
(history; published version)

#11 by Michael De Vlieger at Mon May 16 10:04:13 EDT 2022

STATUS

proposed

approved

#10 by Antti Karttunen at Mon May 16 00:41:47 EDT 2022

STATUS

editing

proposed

#9 by Antti Karttunen at Mon May 16 00:19:33 EDT 2022

LINKS

Antti Karttunen, <a href="/A353813/b353813.txt">Table of n, a(n) for n = 1..100000</a>

STATUS

approved

editing

#8 by Michael De Vlieger at Sun May 15 23:51:15 EDT 2022

STATUS

proposed

approved

#7 by Antti Karttunen at Sun May 15 13:57:18 EDT 2022

STATUS

editing

proposed

#6 by Antti Karttunen at Sun May 15 03:31:43 EDT 2022

FORMULA

a(n) <= A353812(n), a(n) <= A353814(n).

Discussion

Sun May 15

13:57

Antti Karttunen: Thanks Peter.

#5 by Antti Karttunen at Sun May 15 03:29:01 EDT 2022

LINKS

<a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

FORMULA

a(n) <= A353814(n).

#4 by Antti Karttunen at Sun May 15 03:18:58 EDT 2022

CROSSREFS

Cf. A004018, A353814.

#3 by Antti Karttunen at Sat May 14 06:58:05 EDT 2022

PROG

A004018(n) = if(n<1, n==0, 4 * sumdiv( n, d, (d%4==1) - (d%4==3))); \\ From A004018 by _Michael Somos_, Jul 19 2004

Discussion

Sat May 14

08:33

Peter Munn: @Antti. I have responded to your points in A348717.

#2 by Antti Karttunen at Sat May 14 06:55:45 EDT 2022

NAME

allocated for Antti Karttunena(n) = 1 if n has exactly one prime factor of form 4*k+1 (when counted with multiplicity) and no prime factor 4*k+3 with odd multiplicity, otherwise 0.

DATA

0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0

OFFSET

1

FORMULA

a(n) = [A004018(n) == 8], where [ ] is the Iverson bracket.

PROG

(PARI) A353813(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((ep>1)||(nb1>1), return(0))); if((3==(p%4)) && (ep%2), return(0))); return(1==nb1); }; \\ After "isok" function in A230779

(PARI)

A004018(n) = if(n<1, n==0, 4 * sumdiv( n, d, (d%4==1) - (d%4==3))); \\ From A004018 by Michael Somos, Jul 19 2004

A353813(n) = (8==A004018(n));

CROSSREFS

Characteristic function of A230779.

Cf. A004018.

Differs from A353812 for the first time at n=325, where a(325) = 0, while A353812(325) = 1.

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, May 14 2022

STATUS

approved

editing