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Revision History for A373485

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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a(n) = gcd(A083345(n), A276085(n)), where A276085 is fully additive with a(p) = p#/p, and A083345 is the numerator of the fully additive function with a(p) = 1/p.
(history; published version)

#10 by OEIS Server at Sun Jun 09 13:21:17 EDT 2024

LINKS

Antti Karttunen, <a href="/A373485/b373485_1.txt">Table of n, a(n) for n = 1..100000</a>

#9 by Michael De Vlieger at Sun Jun 09 13:21:17 EDT 2024

STATUS

proposed

approved

Discussion

Sun Jun 09

13:21

OEIS Server: Installed first b-file as b373485.txt.

#8 by Antti Karttunen at Sun Jun 09 12:07:36 EDT 2024

STATUS

editing

proposed

#7 by Antti Karttunen at Sun Jun 09 12:06:59 EDT 2024

COMMENTS

For all n >= 2, a(n) divides 1, A373145(n) is a multiple of a(n).

For all i, j: A373151(i) = A373151(j) => a(i) = a(j) => A373483(i) = A373483(j).

CROSSREFS

Cf. A083345, A276085, A373145, A373151.

Cf. A369002 (positions of even terms), A369003 (of odd terms), A373483, A373484 (of multiples of 3).

STATUS

proposed

editing

#6 by Antti Karttunen at Sun Jun 09 05:13:31 EDT 2024

STATUS

editing

proposed

#5 by Antti Karttunen at Sun Jun 09 05:09:14 EDT 2024

CROSSREFS

Cf. A083345, A276085, A373145, A373484 (positions of multiples of 3).

Cf. A369002 (positions of even terms), A369003 (of odd terms), A373484 (of multiples of 3).

#4 by Antti Karttunen at Sun Jun 09 01:03:23 EDT 2024

COMMENTS

For all n >= 2, each a(n) is a divisor of divides A373145(n).

LINKS

Antti Karttunen, <a href="/A373485/b373485_1.txt">Table of n, a(n) for n = 1..100000</a>

#3 by Antti Karttunen at Sun Jun 09 00:59:37 EDT 2024

COMMENTS

For n >= 2, each a(n) is a divisor of A373145(n).

CROSSREFS

Cf. A083345, A276085, A373145, A373484 (positions of multiples of 3).

#2 by Antti Karttunen at Sun Jun 09 00:54:23 EDT 2024

NAME

allocated for Antti Karttunena(n) = gcd(A083345(n), A276085(n)), where A276085 is fully additive with a(p) = p#/p, 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, 7, 1, 4, 1, 1, 8, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 8, 1, 1, 1, 5, 2, 1, 12, 1, 1, 1, 8, 1, 1, 1, 1, 4, 1, 1, 1, 1, 2, 1, 4, 2, 1, 1, 8, 1, 2, 1, 1, 1, 1, 1, 17, 3, 6, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 4, 6, 1, 1, 1, 4, 1, 1, 1, 2, 1, 8, 1, 1, 1, 20, 4, 2, 1, 12, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1

OFFSET

1,8

PROG

(PARI)

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

A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1, primepi(f[k, 1]-1), prime(i))); };

A373485(n) = gcd(A083345(n), A276085(n));

CROSSREFS

Cf. A083345, A276085, A373484 (positions of multiples of 3).

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Jun 09 2024

STATUS

approved

editing

#1 by Antti Karttunen at Thu Jun 06 12:43:46 EDT 2024

NAME

allocated for Antti Karttunen

KEYWORD

allocated

STATUS

approved