A054754 Totient(n) and cototient(n) are squares.

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

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) = 4913-4624 = 289 = 17^2.

a(n) is not an odd power of a prime of A002496, like a(14) = 468, where phi(468) = 144 and 468-phi(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(n-eulerphi(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