The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A247129

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A247129

Semiprimes n such that phi(n) is a square.
(history; published version)

#10 by Charles R Greathouse IV at Thu Nov 20 09:28:56 EST 2014

STATUS

editing

approved

#9 by Charles R Greathouse IV at Thu Nov 20 09:28:53 EST 2014

LINKS

Charles R Greathouse IV, <a href="/A247129/b247129.txt">Table of n, a(n) for n = 1..10000</a>

PROG

(PARI) list(lim)=my(v=List()); forprime(p=2, sqrtint(lim\1), forprime(q=p+1, lim\p, if(issquare((p-1)*(q-1)), listput(v, p*q)))); Set(v)

STATUS

approved

editing

#8 by Bruno Berselli at Thu Nov 20 06:08:01 EST 2014

STATUS

reviewed

approved

#7 by Joerg Arndt at Thu Nov 20 05:50:03 EST 2014

STATUS

proposed

reviewed

#6 by Charles R Greathouse IV at Wed Nov 19 23:43:00 EST 2014

STATUS

editing

proposed

#5 by Charles R Greathouse IV at Wed Nov 19 23:42:52 EST 2014

NAME

allocated for Charles R Greathouse IVSemiprimes n such that phi(n) is a square.

DATA

10, 34, 57, 74, 85, 185, 202, 219, 394, 451, 489, 505, 514, 629, 679, 802, 985, 1057, 1154, 1285, 1354, 1387, 1417, 1717, 2005, 2047, 2509, 2594, 2649, 2761, 2885, 3097, 3202, 3277, 3349, 3385, 3409, 3459, 3737, 4207, 4369, 4377, 4577

OFFSET

1,1

COMMENTS

Freiberg & Pomerance show that this sequence is infinite and a(n) << n^2 log^2 n.

LINKS

Tristan Freiberg, Carl Pomerance, <a href="http://arxiv.org/abs/1410.8109">A note on square totients</a>, arXiv:1410.8109 [math.NT], 2014.

PROG

(PARI) is(n)=issquare(eulerphi(n))&&bigomega(n)==2

CROSSREFS

Cf. A039770, A221285, A002496.

KEYWORD

allocated

nonn

AUTHOR

Charles R Greathouse IV, Nov 19 2014

STATUS

approved

editing

#4 by Charles R Greathouse IV at Wed Nov 19 23:42:52 EST 2014

NAME

allocated for Charles R Greathouse IV

KEYWORD

recycled

allocated

#3 by R. J. Mathar at Fri Nov 14 14:47:12 EST 2014

STATUS

editing

approved

#2 by R. J. Mathar at Fri Nov 14 14:47:09 EST 2014

NAME

allocated for Charles Jwo-Yue Lien

KEYWORD

allocated

recycled

STATUS

approved

editing

#1 by Charles Jwo-Yue Lien at Wed Sep 10 17:25:52 EDT 2014

NAME

allocated for Charles Jwo-Yue Lien

KEYWORD

allocated

STATUS

approved