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

Author

Labos Elemer, Apr 25 2000

Keywords

• nonn

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

Crossrefs

Cf. A000010, A002496, A039770, A051953, A063752.

Programs

Mathematica

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

PARI

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

Formula

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