The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A179877 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A179877

Numbers h such that h and h+1 have same contraharmonic mean of the numbers k < h such that gcd(k, h) = 1 and simultaneously this mean is integer (see A179882).
(history; published version)

#27 by N. J. A. Sloane at Fri Sep 14 04:32:43 EDT 2018

STATUS

proposed

approved

#26 by Michel Marcus at Tue Aug 21 01:25:41 EDT 2018

STATUS

editing

proposed

#25 by Michel Marcus at Tue Aug 21 01:24:46 EDT 2018

EXAMPLE

10 is in the sequence since the reduced residue system of 10 is {1, 3, 7, 9} and that of 11 is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 1 inserted (*-_Hilko Koning_, Aug 20 2018*); the mean of the squares of these 2 systems, divided by the mean of the systems themselves, is 7 in both cases.

6 is not in the sequence, because though the RRS of 6, {1, 5}, and that of 7, {1, 2, 3, 4, 5, 6}, 1 inserted (*-_Hilko Koning_, Aug 20 2018*), have the same contraharmonic mean of 13/3, it is not integral. (End) [corrected by _Hilko Koning_, Aug 20 2018]

STATUS

proposed

editing

Discussion

Tue Aug 21

01:25

Michel Marcus: was not really legible ; not sure an attribution is necessary for such a correction; still I moved it after the example

#24 by Hilko Koning at Tue Aug 21 00:36:50 EDT 2018

STATUS

editing

proposed

#23 by Hilko Koning at Mon Aug 20 04:47:24 EDT 2018

EXAMPLE

STATUS

reviewed

editing

#22 by Michel Marcus at Tue Aug 14 00:31:25 EDT 2018

STATUS

proposed

reviewed

Discussion

Mon Aug 20

03:35

Hilko Koning: rrs[n_Integer?Positive] := Select[Range[n], GCD[#, n] == 1 &]; rrs[7] gives {1, 2, 3, 4, 5, 6} and ContraharmonicMean[{1, 2, 3, 4, 5, 6}] is 13/3
rrs[n_Integer?Positive] := Select[Range[n], GCD[#, n] == 1 &]; rrs[11] gives {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and ContraharmonicMean[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}] is 7
or see if necessary https://youtu.be/5RQY9zj-Nng?t=166

#21 by Hilko Koning at Tue Aug 14 00:29:43 EDT 2018

STATUS

editing

proposed

#20 by Hilko Koning at Tue Aug 14 00:26:24 EDT 2018

EXAMPLE

6 is not in the sequence, because though the RRS of 6, {1, 5}, and that of 7, {1, 2, 3, 4, 5, 6}, have the same contraharmonic mean of 13/3, it is not integral. (End)

STATUS

reviewed

editing

Discussion

Tue Aug 14

00:29

Hilko Koning: rrs[n_Integer?Positive] := Select[Range[n], GCD[#, n] == 1 &];
rrs[7] 
 is
{1, 2, 3, 4, 5, 6} and
rrs[n_Integer?Positive] := Select[Range[n], GCD[#, n] == 1 &];
rrs[11]
 is
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

#19 by Michel Marcus at Mon Aug 13 05:44:19 EDT 2018

STATUS

proposed

reviewed

#18 by Michel Marcus at Fri Aug 03 03:23:17 EDT 2018

STATUS

editing

proposed

Discussion

Fri Aug 03

03:47

Hilko Koning: ok