The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A373377 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A373377

a(n) = gcd(A059975(n), A083345(n)), where A059975 is fully additive with a(p) = p-1, and A083345 is the numerator of the fully additive function with a(p) = 1/p.
(history; published version)

#7 by OEIS Server at Wed Jun 05 19:23:09 EDT 2024

LINKS

Antti Karttunen, <a href="/A373377/b373377_1.txt">Table of n, a(n) for n = 1..65537</a>

#6 by Michael De Vlieger at Wed Jun 05 19:23:09 EDT 2024

STATUS

proposed

approved

Discussion

Wed Jun 05

19:23

OEIS Server: Installed first b-file as b373377.txt.

#5 by Antti Karttunen at Wed Jun 05 15:54:56 EDT 2024

STATUS

editing

proposed

#4 by Antti Karttunen at Wed Jun 05 15:43:03 EDT 2024

COMMENTS

For each n >= 2, a(n) is a divisor of A373378(n).

LINKS

Antti Karttunen, <a href="/A373377/b373377_1.txt">Table of n, a(n) for n = 1..65537</a>

#3 by Antti Karttunen at Wed Jun 05 15:38:54 EDT 2024

COMMENTS

For n >= 2, a(n) is a divisor of A373378(n).

#2 by Antti Karttunen at Wed Jun 05 15:32:36 EDT 2024

NAME

allocated for Antti Karttunena(n) = gcd(A059975(n), A083345(n)), where A059975 is fully additive with a(p) = p-1, and A083345 is the numerator of the fully additive function with a(p) = 1/p.

DATA

0, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 4, 1, 1, 2, 2, 1, 1, 1, 6, 2, 1, 1, 1, 2, 1, 1, 8, 1, 1, 1, 5, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 12, 1, 1, 1, 1, 2, 9, 2, 14, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 18, 2, 1, 1, 1, 1, 1, 1, 20, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 24, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

OFFSET

1,8

PROG

(PARI)

A059975(n) = { my(f = factor(n)); sum(i = 1, #f~, f[i, 2]*(f[i, 1] - 1)); };

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

A373377(n) = gcd(A059975(n), A083345(n));

CROSSREFS

Cf. A059975, A083345.

Cf. A369002 (positions of even terms), A369003 (of odd terms).

Cf. also A373363, A373368, A373369, A373378.

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Jun 05 2024

STATUS

approved

editing

#1 by Antti Karttunen at Sun Jun 02 15:03:11 EDT 2024

NAME

allocated for Antti Karttunen

KEYWORD

allocated

STATUS

approved