

A054754


Totient(n) and cototient(n) are squares.


5



1, 2, 5, 8, 17, 32, 37, 101, 125, 128, 197, 257, 401, 468, 512, 577, 677, 1297, 1417, 1601, 1872, 2048, 2340, 2917, 3125, 3137, 3145, 4100, 4212, 4357, 4913, 5477, 7057, 7488, 8101, 8192, 8837, 9360, 12101, 13457, 14401, 14841, 15377, 15588, 15877
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OFFSET

1,2


COMMENTS

Subsequence of A039770, supersequence of A002496.
a(n) is an odd power of a prime q = w^2+1, like 4913 = 17^3, where A000010(a(31)) = phi(4913) = 4624 = 68^2 and A051953(4913) = 49134624 = 289 = 17^2.
a(n) is not an odd power of a prime of A002496, like a(14) = 468, where phi(468) = 144 and 468phi(468) = 324 = 18^2.
Intersection of A039770 and A063752.  Altug Alkan, Aug 16 2017


LINKS

Donovan Johnson, Table of n, a(n) for n = 1..10000


FORMULA

A000010(a(n))=x^2 and a(n)A000010(a(n))=y^2.


MATHEMATICA

Select[Range@ 16000, Function[n, AllTrue[{#, n  #} &@ EulerPhi@ n, IntegerQ@ Sqrt@ # &]]] (* Michael De Vlieger, Aug 16 2017 *)


PROG

(PARI) isok(n) = issquare(eulerphi(n)) && issquare(neulerphi(n)); \\ Michel Marcus, Sep 09 2013


CROSSREFS

Cf. A000010, A002496, A039770, A051953, A063752.
Sequence in context: A285459 A259580 A316795 * A054755 A093331 A162216
Adjacent sequences: A054751 A054752 A054753 * A054755 A054756 A054757


KEYWORD

nonn


AUTHOR

Labos Elemer, Apr 25 2000


STATUS

approved



