The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A369975

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A369975

Parity of A369974.
(history; published version)

#9 by OEIS Server at Fri Feb 09 15:49:39 EST 2024

LINKS

Antti Karttunen, <a href="/A369975/b369975_1.txt">Table of n, a(n) for n = 1..65537</a>

#8 by Michael De Vlieger at Fri Feb 09 15:49:39 EST 2024

STATUS

proposed

approved

Discussion

Fri Feb 09

15:49

OEIS Server: Installed first b-file as b369975.txt.

#7 by Antti Karttunen at Fri Feb 09 12:53:25 EST 2024

STATUS

editing

proposed

#6 by Antti Karttunen at Fri Feb 09 12:48:30 EST 2024

FORMULA

a(n) <= A369001(n). [Because A369002 is a multiplicative semigroup; proof is similar to one given in A359780.]

CROSSREFS

Cf. also A359780.

#5 by Antti Karttunen at Fri Feb 09 12:40:42 EST 2024

FORMULA

a(n) = A369974(n) mod 2 = A369978(n) mod 2.

CROSSREFS

Parity of A369974 and of A369978.

Cf. A083345, A369002, A369974.

#4 by Antti Karttunen at Fri Feb 09 12:15:00 EST 2024

LINKS

Antti Karttunen, <a href="/A369975/b369975_1.txt">Table of n, a(n) for n = 1..65537</a>

#3 by Antti Karttunen at Fri Feb 09 12:08:57 EST 2024

FORMULA

a(n) <= A369001(n). [Because A369002 is a multiplicative semigroup.]

CROSSREFS

Cf. A083345, A369002, A369974.

#2 by Antti Karttunen at Fri Feb 09 12:06:34 EST 2024

NAME

allocated for Antti Karttunen

Parity of A369974.

DATA

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

OFFSET

1

LINKS

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

FORMULA

a(n) = A369974(n) mod 2.

PROG

(PARI)

A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };

A369001(n) = !(A083345(n)%2);

memoA369974 = Map();

A369974(n) = if(1==n, 1, my(v); if(mapisdefined(memoA369974, n, &v), v, v = -sumdiv(n, d, if(d<n, A369001(n/d)*A369974(d), 0)); mapput(memoA369974, n, v); (v)));

A369975(n) = (A369974(n)%2);

CROSSREFS

Characteristic function of A369976.

Cf. A083345, A369974.

Differs from A369001 for the first time at n=81, where a(81) = 0, while A369001(81) = 1.

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Feb 09 2024

STATUS

approved

editing

#1 by Antti Karttunen at Wed Feb 07 04:24:50 EST 2024

NAME

allocated for Antti Karttunen

KEYWORD

allocated

STATUS

approved