The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A373364 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A373364

a(n) = gcd(A001414(n), A003415(n)), where A001414 is the sum of prime factors with repetition, and A003415 is the arithmetic derivative.
(history; published version)

#10 by Michael De Vlieger at Tue Jun 04 07:39:33 EDT 2024

STATUS

proposed

approved

#9 by Antti Karttunen at Tue Jun 04 07:23:06 EDT 2024

STATUS

editing

proposed

#8 by Antti Karttunen at Tue Jun 04 02:22:48 EDT 2024

CROSSREFS

Cf. A001414, A003415, A373375 (positions of even terms), A373376 (of odd terms).

STATUS

approved

editing

#7 by OEIS Server at Mon Jun 03 00:27:05 EDT 2024

LINKS

Antti Karttunen, <a href="/A373364/b373364_1.txt">Table of n, a(n) for n = 1..65537</a>

#6 by Michael De Vlieger at Mon Jun 03 00:27:05 EDT 2024

STATUS

proposed

approved

Discussion

Mon Jun 03

00:27

OEIS Server: Installed first b-file as b373364.txt.

#5 by Antti Karttunen at Sun Jun 02 21:48:44 EDT 2024

STATUS

editing

proposed

#4 by Antti Karttunen at Sun Jun 02 21:47:33 EDT 2024

COMMENTS

For n >= 2, 1, a(n) is a multiple of A373363(n).

LINKS

Antti Karttunen, <a href="/A373364/b373364_1.txt">Table of n, a(n) for n = 1..65537</a>

#3 by Antti Karttunen at Sun Jun 02 21:15:23 EDT 2024

COMMENTS

For n >= 2, a(n) is a multiple of A373363(n).

#2 by Antti Karttunen at Sun Jun 02 21:11:57 EDT 2024

NAME

allocated for Antti Karttunena(n) = gcd(A001414(n), A003415(n)), where A001414 is the sum of prime factors with repetition, and A003415 is the arithmetic derivative.

DATA

0, 1, 1, 4, 1, 5, 1, 6, 6, 7, 1, 1, 1, 9, 8, 8, 1, 1, 1, 3, 10, 13, 1, 1, 10, 15, 9, 1, 1, 1, 1, 10, 14, 19, 12, 10, 1, 21, 16, 1, 1, 1, 1, 3, 1, 25, 1, 1, 14, 3, 20, 1, 1, 1, 16, 1, 22, 31, 1, 4, 1, 33, 1, 12, 18, 1, 1, 3, 26, 1, 1, 12, 1, 39, 1, 1, 18, 1, 1, 1, 12, 43, 1, 2, 22, 45, 32, 1, 1, 1, 20, 3, 34, 49, 24

OFFSET

1,4

PROG

(PARI)

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

A373364(n) = gcd(A001414(n), A003415(n));

CROSSREFS

Cf. A001414, A003415.

Cf. also A082299, A373362, A373363.

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Jun 02 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