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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

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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) = 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.