The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A374106

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a(n) = gcd(A113177(n), A328845(n)), where A113177 is fully additive with a(p) = Fibonacci(p) and A328845 is the first Fibonacci-based variant of the arithmetic derivative.
(history; published version)

#8 by OEIS Server at Fri Jun 28 14:54:36 EDT 2024

LINKS

Antti Karttunen, <a href="/A374106/b374106_1.txt">Table of n, a(n) for n = 1..4500</a>

#7 by Michael De Vlieger at Fri Jun 28 14:54:36 EDT 2024

STATUS

proposed

approved

Discussion

Fri Jun 28

14:54

OEIS Server: Installed first b-file as b374106.txt.

#6 by Antti Karttunen at Fri Jun 28 14:37:27 EDT 2024

STATUS

editing

proposed

#5 by Antti Karttunen at Fri Jun 28 14:36:34 EDT 2024

LINKS

Antti Karttunen, <a href="/A374106/b374106_1.txt">Table of n, a(n) for n = 1..4500</a>

#4 by Antti Karttunen at Fri Jun 28 14:33:07 EDT 2024

FORMULA

For all n >= 1, a(A000040(n)) = A030426(n).

CROSSREFS

Cf. A000040, A000045, A030426, A113177, A328845.

#3 by Antti Karttunen at Fri Jun 28 14:31:14 EDT 2024

NAME

allocated for Antti Karttunena(n) = gcd(A113177(n), A328845(n)), where A113177 is fully additive with a(p) = Fibonacci(p) and A328845 is the first Fibonacci-based variant of the arithmetic derivative.

DATA

0, 1, 2, 2, 5, 1, 13, 3, 4, 3, 89, 4, 233, 1, 1, 4, 1597, 1, 4181, 1, 1, 9, 28657, 1, 10, 1, 6, 5, 514229, 1, 1346269, 5, 1, 1, 2, 6, 24157817, 17, 5, 4, 165580141, 1, 433494437, 1, 3, 7, 2971215073, 2, 26, 1, 1, 1, 53316291173, 1, 2, 4, 1, 3, 956722026041, 1, 2504730781961, 1, 1, 6, 2, 1, 44945570212853, 3, 1, 1

OFFSET

1,3

PROG

(PARI)

A113177(n) = if(n<=1, 0, my(f=factor(n)); sum(i=1, #f~, f[i, 2]*fibonacci(f[i, 1])));

A328845(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*fibonacci(f[i, 1])/f[i, 1]));

A374106(n) = gcd(A113177(n), A328845(n));

CROSSREFS

Cf. A000045, A113177, A328845.

Cf. also A374035.

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Jun 28 2024

STATUS

approved

editing

#2 by Antti Karttunen at Fri Jun 28 14:20:49 EDT 2024

KEYWORD

allocating

allocated

#1 by Antti Karttunen at Fri Jun 28 14:20:49 EDT 2024

NAME

allocated for Antti Karttunen

KEYWORD

allocating

STATUS

approved