The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A051953

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A051953

Cototient(n) := n - phi(n).
(history; published version)

#119 by N. J. A. Sloane at Fri Oct 06 10:57:41 EDT 2023

STATUS

proposed

approved

#118 by Antti Karttunen at Fri Oct 06 04:20:13 EDT 2023

STATUS

editing

proposed

#117 by Antti Karttunen at Fri Oct 06 04:19:36 EDT 2023

COMMENTS

Let S be the sum of the cototients of the divisors of n (A001065). S < n iff n is deficient, S = n iff n is perfect, and S > n iff n is abundant. - Ivan N. Ianakiev, Oct 06 2023

CROSSREFS

Cf. A000010, A001065, (inverse Möbius transform), A005278, A001274, A083254, A098006, A049586, A051612, A053579, A054525, A062790 (Möbius transform), A063985 (partial sums), A063986, A290087.

STATUS

proposed

editing

Discussion

Fri Oct 06

04:20

Antti Karttunen: That explains it fully...

#116 by Ivan N. Ianakiev at Fri Oct 06 04:16:14 EDT 2023

STATUS

editing

proposed

#115 by Ivan N. Ianakiev at Fri Oct 06 04:16:00 EDT 2023

COMMENTS

Let S be the sum of the cototients of the divisors of n. S < n iff n is deficient, S = n iff n is perfect, and S > n iff n is abundant. - Ivan N. Ianakiev, Oct 06 2023

STATUS

approved

editing

#114 by Michael De Vlieger at Fri Apr 29 12:02:07 EDT 2022

STATUS

proposed

approved

#113 by Antti Karttunen at Fri Apr 29 10:33:12 EDT 2022

STATUS

editing

proposed

#112 by Antti Karttunen at Fri Apr 29 10:32:34 EDT 2022

FORMULA

a(n) = A051612(n) - A001065(n).

CROSSREFS

Cf. A000010, A001065, A005278, A001274, A083254, A098006, A049586, A051612, A053579, A054525, A062790 (Möbius transform), A063985 (partial sums), A063986, A290087.

#111 by Antti Karttunen at Fri Apr 29 10:30:23 EDT 2022

STATUS

proposed

editing

#110 by Antti Karttunen at Fri Apr 29 10:29:59 EDT 2022

STATUS

editing

proposed