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A262406 Squarefree k such that phi(k) is a perfect square. 3
1, 2, 5, 10, 17, 34, 37, 57, 74, 85, 101, 114, 170, 185, 197, 202, 219, 257, 273, 285, 370, 394, 401, 438, 451, 489, 505, 514, 546, 570, 577, 629, 677, 679, 802, 902, 969, 978, 985, 1010, 1057, 1095, 1154, 1258, 1285, 1297, 1354, 1358, 1365 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The subsequence of primes is A002496 (primes of the form k^2+1). - Michel Marcus, Oct 14 2015

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

W. D. Banks, J. B. Friedlander, C. Pomerance and I. E. Shparlinski, Multiplicative structure of values of the Euler function, in High Primes and Misdemeanours: Lectures in Honour of the Sixtieth Birthday of Hugh Cowie Williams (A. Van der Poorten, ed.), Fields Inst. Comm. 41 (2004), pp. 29-47.

FORMULA

Banks, Friedlander, Pomerance, and Shparlinski show that a(n) = O(n^1.421).

PROG

(PARI) is(n)=my(f=factor(n)); issquare(eulerphi(f)) && (n==1 || vecmax(f[, 2])==1)

(MAGMA) [n: n in [1..1400] | IsSquarefree(n) and IsSquare(EulerPhi(n))]; // Vincenzo Librandi, May 05 2016

CROSSREFS

Intersection of A039770 and A005117.

Cf. A000010, A002496, A007614, A068560, A004171, A114063.

Sequence in context: A107482 A227363 A342172 * A308600 A308604 A018315

Adjacent sequences:  A262403 A262404 A262405 * A262407 A262408 A262409

KEYWORD

nonn

AUTHOR

Charles R Greathouse IV, Oct 13 2015

STATUS

approved

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Last modified July 29 23:58 EDT 2021. Contains 346346 sequences. (Running on oeis4.)