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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 25 14:47 EST 2020. Contains 338625 sequences. (Running on oeis4.)