The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A306711 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A306711

Numbers k such that gcd(k, phi(k)) <> gcd(k, psi(k)).
(history; published version)

#27 by Susanna Cuyler at Sun Apr 28 20:08:57 EDT 2019

STATUS

proposed

approved

#26 by Robert Israel at Sun Apr 28 17:34:07 EDT 2019

STATUS

editing

proposed

#25 by Robert Israel at Sun Apr 28 17:34:02 EDT 2019

LINKS

Robert Israel, <a href="/A306711/b306711.txt">Table of n, a(n) for n = 1..10000</a>

MAPLE

psi:= k -> mul((t+1)/t, t=numtheory:-factorset(k))*k:

select(t -> igcd(t, psi(t)) <> igcd(t, numtheory:-phi(t)), [$1..1000]); # Robert Israel, Apr 28 2019

STATUS

approved

editing

#24 by Bruno Berselli at Fri Apr 26 02:32:42 EDT 2019

STATUS

reviewed

approved

#23 by Michel Marcus at Fri Apr 26 00:46:24 EDT 2019

STATUS

proposed

reviewed

#22 by Michel Marcus at Sun Apr 14 13:28:09 EDT 2019

STATUS

editing

proposed

#21 by Michel Marcus at Sun Apr 14 13:28:05 EDT 2019

COMMENTS

Numbers m such that A306695(m) = m is an elementare terms.

STATUS

proposed

editing

#20 by Michel Marcus at Thu Mar 21 00:38:54 EDT 2019

STATUS

editing

proposed

#19 by Michel Marcus at Thu Mar 21 00:38:50 EDT 2019

PROG

(PARI) dpsi(n) = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615

isok(k) = gcd(k, eulerphi(k)) != gcd(k, dpsi(k)); \\ Michel Marcus, Mar 21 2019

#18 by Torlach Rush at Mon Mar 11 15:53:18 EDT 2019

COMMENTS

The ratio gcd(k, phi(k)) : gcd(k, psi(k)), when reduced, contains at least one prime number that divides a(n).

STATUS

proposed

editing

Discussion

Mon Mar 18

17:40

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