A039770 -id:A039770 - cp's OEIS frontend

A062732 Squares arising in A039770.

1, 1, 4, 4, 4, 4, 16, 16, 16, 36, 16, 16, 36, 16, 36, 36, 36, 64, 100, 36, 36, 100, 36, 64, 64, 64, 64, 144, 64, 196, 100, 64, 144, 64, 100, 256, 144, 144, 144, 144, 144, 144, 144, 144, 144, 196, 400, 144, 144, 144, 400, 144, 144, 324, 144, 400, 256, 324, 256, 144

Offset: 1

Jason Earls, Jul 12 2001

nonn

D. M. Burton, Elementary Number Theory, Allyn and Bacon Inc., Boston MA, 1976, p. 141.

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A039770.

je=[]; for(n=1,1000, if(issquare(eulerphi(n)),je=concat(je,eulerphi(n)))); je

n=0; for (m=1, 10^5, if (issquare(a=eulerphi(m)), write("b062732.txt", n++, " ", a); if (n==1000, break))) \\ Harry J. Smith, Aug 10 2009

A002496 Primes of the form k^2 + 1.

Original entry on oeis.org

2, 5, 17, 37, 101, 197, 257, 401, 577, 677, 1297, 1601, 2917, 3137, 4357, 5477, 7057, 8101, 8837, 12101, 13457, 14401, 15377, 15877, 16901, 17957, 21317, 22501, 24337, 25601, 28901, 30977, 32401, 33857, 41617, 42437, 44101, 50177

Offset: 1

N. J. A. Sloane

It is conjectured that this sequence is infinite, but this has never been proved.
An equivalent description: primes of form P = (p1*p2*...*pm)^k + 1 where p1..pm are primes and k > 1, since then k must be even for P to be prime.
Also prime = p(n) if A054269(n) = 1, i.e., quotient-cycle-length = 1 in continued fraction expansion of sqrt(p). - Labos Elemer, Feb 21 2001
Also primes p such that phi(p) is a square.
Also primes of form x*y + z, where x, y and z are three successive numbers. - Giovanni Teofilatto, Jun 05 2004
It is a result that goes back to Mirsky that the set of primes p for which p-1 is squarefree has density A, where A = A005596 denotes the Artin constant. More precisely, Sum_{p <= x} mu(p-1)^2 = A*x/log x + o(x/log x) as x tends to infinity. Conjecture: Sum_{p <= x, mu(p-1)=1} 1 = (A/2)*x/log x + o(x/log x) and Sum_{p <= x, mu(p-1)=-1} 1 = (A/2)*x/log x + o(x/log x). - Pieter Moree (moree(AT)mpim-bonn.mpg.de), Nov 03 2003
Also primes of the form x^y + 1, where x > 0, y > 1. Primes of the form x^y - 1 (x > 0, y > 1) are the Mersenne primes listed in A000668(n) = {3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ...}. - Alexander Adamchuk, Mar 04 2007
With the exception of the first two terms {2,5}, the continued fraction (1 + sqrt(p))/2 has period 3. - Artur Jasinski, Feb 03 2010
With the exception of the first term {2}, congruent to 1 (mod 4). - Artur Jasinski, Mar 22 2011
With the exception of the first two terms, congruent to 1 or 17 (mod 20). - Robert Israel, Oct 14 2014
From Bernard Schott, Mar 22 2019: (Start)
These primes are the primitive terms which generate the sequence of integers with only one prime factor and whose Euler's totient is a square: A054755. So this sequence is a subsequence of A054755 and of A039770. Additionally, the terms of this sequence also have a square cototient, so this sequence is a subsequence of A063752 and A054754.
If p prime = n^2 + 1, phi(p) = n^2 and cototient(p) = 1^2.
Except for 3, the four Fermat primes in A019434 {5, 17, 257, 65537}, belong to this sequence; with F_k = 2^(2^k) + 1, phi(F_k) = (2^(2^(k-1)))^2.
See the file "Subfamilies and subsequences" (& I) in A039770 for more details, proofs with data, comments, formulas and examples. (End)
In this sequence, primes ending with 7 seem to appear twice as often as primes ending with 1. This is because those with 7 come from integers ending with 4 or 6, while those with 1 come only from integers ending with 0 (see De Koninck & Mercier reference). - Bernard Schott, Nov 29 2020
The set of odd primes p for which every elliptic curve of the form y^2 = x^3 + d*x has order p-1 over GF(p) for those d with (d,p)=1 and d a fourth power modulo p. - Gary Walsh, Sep 01 2021 [edited, Gary Walsh, Apr 26 2025]

Jean-Marie De Koninck & Armel Mercier, 1001 Problèmes en Théorie Classique des Nombres, Problème 211 pp. 34 and 169, Ellipses, Paris, 2004.
Leonhard Euler, De numeris primis valde magnis (E283), reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 3, p. 22.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 17.
Hugh L. Montgomery, Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, Amer. Math. Soc., 1996, p. 208.
C. Stanley Ogilvy, Tomorrow's Math. 2nd ed., Oxford Univ. Press, 1972, p. 116.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 118.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Rev. ed. 1997), p. 134.

T. D. Noe, Table of n, a(n) for n = 1..10000
Tewodros Amdeberhan, Luis A. Medina and Victor H. Moll, Arithmetical properties of a sequence arising from an arctangent sum, J. Numb. Theory, Vol. 128, No. 6 (2008), pp. 1807-1846, eq. (1.10).
William D. Banks, John B. Friedlander, Carl Pomerance and Igor E. Shparlinski, Multiplicative structure of values of the Euler function, in High Primes and Misdemeanours: Lectures in Honour of the Sixtieth Birthday of Hugh Cowie Williams (A. Van der Poorten, ed.), Fields Inst. Comm. 41 (2004), pp. 29-47.
Paul T. Bateman and Roger A. Horn, A heuristic asymptotic formula concerning the distribution of prime numbers, Mathematics of Computation, Vol. 16, No. 79 (1962), pp. 363-367.
Joel E. Cohen, Conjectures about Primes and Cyclic Numbers, arXiv:2508.08335 [math.NT], 2025. See p. 11.
Frank Ellermann, Primes of the form (m^2)+1 up to 10^6.
Dan Ismailescu and Yunkyu James Lee, Polynomially growing integer sequences all whose terms are composite, arXiv:2501.04851 [math.NT], 2025. See p. 9.
Leon Mirsky, The number of representations of an integer as the sum of a prime and a k-free integer, Amer. Math. Monthly, Vol. 56, No. 1 (1949), pp. 17-19.
Maxie D. Schmidt, New Congruences and Finite Difference Equations for Generalized Factorial Functions, arXiv:1701.04741 [math.CO], 2017.
Apoloniusz Tyszka, On sets X subset of N for which we know an algorithm that computes a threshold number t(X) in N such that X is infinite if and only if X contains an element greater than t(X), 2019.
Apoloniusz Tyszka and Sławomir Kurpaska, Open problems that concern computable sets X, subset of N, and cannot be formally stated as they refer to current knowledge about X, (2020).
Eric Weisstein's World of Mathematics, Landau's Problems.
Eric Weisstein's World of Mathematics, Near-Square Prime.
Wikipedia, Bateman-Horn Conjecture.
Marek Wolf, Search for primes of the form m^2+1, arXiv:0803.1456 [math.NT], 2008-2010.

Cf. A083844 (number of these primes < 10^n), A199401 (growth constant).
Cf. A001912, A005574, A054964, A062325, A088179, A090693, A141293, A172168.
Cf. A000668 (Mersenne primes), A019434 (Fermat primes).
Subsequence of A039770.
Cf. A010051, subsequence of A002522.
Cf. A237040 (an analog for n^3 + 1).
Cf. A010051, A000290; subsequence of A028916.
Subsequence of A039770, A054754, A054755, A063752.
Primes of form n^2+b^4, b fixed: A243451 (b=2), A256775 (b=3), A256776 (b=4), A256777 (b=5), A256834 (b=6), A256835 (b=7), A256836 (b=8), A256837 (b=9), A256838 (b=10), A256839 (b=11), A256840 (b=12), A256841 (b=13).
Cf. A030430 (primes ending with 1), A030432 (primes ending with 7).

a002496 n = a002496_list !! (n-1)
a002496_list = filter ((== 1) . a010051') a002522_list
-- Reinhard Zumkeller, May 06 2013

[p: p in PrimesUpTo(100000)| IsSquare(p-1)]; // Vincenzo Librandi, Apr 09 2011

select(isprime, [2, seq(4*i^2+1, i= 1..1000)]); # Robert Israel, Oct 14 2014

Select[Range[100]^2+1, PrimeQ]
Join[{2},Select[Range[2,300,2]^2+1,PrimeQ]] (* Harvey P. Dale, Dec 18 2018 *)

isA002496(n) = isprime(n) && issquare(n-1) \\ Michael B. Porter, Mar 21 2010

is_A002496(n)=issquare(n-1)&&isprime(n) \\ For "random" numbers in the range 10^10 and beyond, at least 5 times faster than the above. - M. F. Hasler, Oct 14 2014

# Python 3.2 or higher required
from itertools import accumulate
from sympy import isprime
A002496_list = [n+1 for n in accumulate(range(10**5),lambda x,y:x+2*y-1) if isprime(n+1)] # Chai Wah Wu, Sep 23 2014

# Python 2.4 or higher required
from sympy import isprime
A002496_list = list(filter(isprime, (n*n+1 for n in range(10**5)))) # David Radcliffe, Jun 26 2016

There are O(sqrt(n)/log(n)) terms of this sequence up to n. But this is just an upper bound. See the Bateman-Horn or Wolf papers, for example, for the conjectured for what is believed to be the correct density.
a(n) = 1 + A005574(n)^2. - R. J. Mathar, Jul 31 2015
Sum_{n>=1} 1/a(n) = A172168. - Amiram Eldar, Nov 14 2020
a(n+1) = 4*A001912(n)^2 + 1. - Hal M. Switkay, Apr 03 2022

Formula, reference, and comment from Charles R Greathouse IV, Aug 24 2009

Edited by M. F. Hasler, Oct 14 2014

A037896 Primes of the form k^4 + 1.

Original entry on oeis.org

2, 17, 257, 1297, 65537, 160001, 331777, 614657, 1336337, 4477457, 5308417, 8503057, 9834497, 29986577, 40960001, 45212177, 59969537, 65610001, 126247697, 193877777, 303595777, 384160001, 406586897, 562448657, 655360001, 723394817, 916636177, 1049760001, 1416468497

Offset: 1

Donald S. McDonald, Feb 27 2000

From Bernard Schott, Apr 22 2019: (Start)
These primes are the primitive terms which generate the sequence of integers with only one prime factor and whose Euler's totient is a perfect biquadrate: A307690, so this sequence is a subsequence of A078164 and A307690.
If p prime = k^4 + 1, phi(p) = k^4.
The last three Fermat primes in A019434 {17, 257, 65537} belong to this sequence; with F_k = 2^(2^k) + 1 and for k = 2, 3, 4, phi(F_k) = (2^(2^(k-2)))^4. (End)

			6^4 + 1 = 1297 is prime.

T. D. Noe, Table of n, a(n) for n=1..1000
Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
M. Lal, Primes of the form n^4 + 1, Math. Comp. 21 (1967), pp. 245-247.

Cf. A000068, A002523, A019434, A078164, A307690.

Subsequence of A002496, A078164 and A039770.

[n^4+1: n in [1..200] | IsPrime(n^4+1)]; // G. C. Greubel, Apr 28 2019

Select[Range[200]^4+1,PrimeQ] (* Harvey P. Dale, Jul 20 2015 *)

j=[]; for(n=1,200, if(isprime(n^4+1),j=concat(j,n^4+1))); j

list(lim)=my(v=List([2]),p); forstep(k=2,sqrtnint(lim\1-1,4),2, if(isprime(p=k^4+1), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Mar 31 2022

[n^4+1 for n in (1..200) if is_prime(n^4+1)] # G. C. Greubel, Apr 28 2019

a(n) = A002523(A000068(n)). - Elmo R. Oliveira, Feb 21 2025

Corrected and extended by Jason Earls, Jul 19 2001

A078164 Numbers k such that phi(k) is a perfect biquadrate.

Original entry on oeis.org

1, 2, 17, 32, 34, 40, 48, 60, 257, 512, 514, 544, 640, 680, 768, 816, 960, 1020, 1297, 1387, 1417, 1729, 1971, 2109, 2223, 2289, 2331, 2445, 2457, 2565, 2594, 2608, 2774, 2812, 2834, 2835, 3052, 3260, 3458, 3888, 3912, 3924, 3942, 3996, 4104, 4212, 4218

Offset: 1

Labos Elemer, Nov 27 2002

nonn

Corresponding values of phi include 1, 16, 256, 1296, 4096, ... and these arise several times each.
a(3) = A053576(4).
A013776 is a subsequence since phi(2^(4*n+1)) = (2^n)^4. - Bernard Schott, Sep 22 2022
Subsequence of primes is A037896 since in this case: phi(k^4+1) = k^4. - Bernard Schott, Mar 05 2023

Amiram Eldar, Table of n, a(n) for n = 1..10000

Subsequence of A039770. A037896 is a subsequence.
Sequences where phi(k) is a perfect power: A039770 (square), A039771 (cube), this sequence (4th), A078165 (5th), A078166 (6th), A078167 (7th), A078168 (8th), A078169 (9th), A078170 (10th).
Cf. A001317, A053576, A037896, A045544, A000010, A013776.

k=4; Do[s=EulerPhi[n]^(1/k); If[IntegerQ[s], Print[n]], {n, 1, 5000}]
Select[Range[5000],IntegerQ[Surd[EulerPhi[#],4]]&] (* Harvey P. Dale, Apr 30 2015 *)

is(n)=ispower(eulerphi(n),4) \\ Charles R Greathouse IV, Apr 24 2020

from itertools import count, islice
from sympy import totient, integer_nthroot
def A078164_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:integer_nthroot(totient(n),4)[1], count(max(1,startvalue)))
A078164_list = list(islice(A078164_gen(),20)) # Chai Wah Wu, Feb 28 2023

A039771 Numbers k such that phi(k) is a perfect cube.

Original entry on oeis.org

1, 2, 15, 16, 20, 24, 30, 85, 128, 136, 160, 170, 192, 204, 240, 247, 259, 327, 333, 351, 399, 405, 436, 494, 518, 532, 648, 654, 666, 684, 702, 756, 771, 798, 810, 1024, 1028, 1088, 1111, 1255, 1280, 1360, 1375, 1536, 1542, 1632, 1843, 1853, 1875, 1920, 2008

Offset: 1

Olivier Gérard

a(n) is prime only for a(2)=2, for other cases: eulerphi(p) = p-1 = n^3, and p = 1 + n^3 = (n+1)(n^2-n+1), so p cannot be a prime. - Enrique Pérez Herrero, Aug 29 2010

A013730 is a subsequence. - Enrique Pérez Herrero, Aug 29 2010

			phi(247) = 216 = 6*6*6.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2500 from E. Pérez Herrero)

Cf. A000010, A007614, A039770, A216412.

q:= n-> (c-> iroot(c, 3)^3=c)(numtheory[phi](n)):
select(q, [$1..2200])[];  # Alois P. Heinz, Sep 01 2025

Select[ Range[ 2000 ], IntegerQ[ Power[ EulerPhi[ # ], 1/3 ] ]& ]

for(n=1,1e4,if(ispower(eulerphi(n),3),print1(n", "))) \\ Charles R Greathouse IV, Jul 31 2011

A054755 Odd powers of primes of the form q = x^2 + 1 (A002496).

Original entry on oeis.org

2, 5, 8, 17, 32, 37, 101, 125, 128, 197, 257, 401, 512, 577, 677, 1297, 1601, 2048, 2917, 3125, 3137, 4357, 4913, 5477, 7057, 8101, 8192, 8837, 12101, 13457, 14401, 15377, 15877, 16901, 17957, 21317, 22501, 24337, 25601, 28901, 30977, 32401

Offset: 1

Labos Elemer, Apr 25 2000

nonn

A002496 is a subset; the odd power exponent is 1.
From Bernard Schott, Mar 16 2019: (Start)
The terms of this sequence are exactly the integers with only one prime factor and whose Euler's totient is square, so this sequence is a subsequence of A039770. The primitive terms of this sequence are the primes of the form q = x^2 + 1, which are exactly in A002496.
Additionally, the terms of this sequence also have a square cototient, so this sequence is a subsequence of A063752 and A054754.
If q prime = x^2 + 1, phi(q) = x^2, phi(q^(2k+1)) = (x*q^k)^2, and cototient(q) = 1^2, cototient(q^(2k+1)) = (q^k)^2. (End)

			a(20) = 3125 = 5^5, q = 5 = 4^2+1 and Phi(3125) = 2500 = 50^2, cototient(3125) = 3125 - Phi(3125) = 625 = 25^2.

David A. Corneth, Table of n, a(n) for n = 1..18864 (terms <= 10^11)
Bernard Schott, Subfamilies and subsequences

Cf. A000010, A051953, A039770, A063752, A054754, A334745 (with 2 distinct prime factors), A306908 (with 3 distinct prime factors).

Subsequences: A002496 (primitive primes: m^2+1), A004171 (2^(2k+1)), A013710 (5^(2k+1)), A013722 (17^(2k+1)), A262786 (37^(2k+1)).

Select[Range[10^5], And[PrimeNu@ # == 1, IntegerQ@ Sqrt@ EulerPhi@ #] &] (* Michael De Vlieger, Mar 31 2019 *)

isok(m) = (omega(m)==1) && issquare(eulerphi(m)); \\ Michel Marcus, Mar 16 2019

upto(n) = {my(res = List([2]), q); forstep(i = 2, sqrtint(n), 2, if(isprime(i^2 + 1), listput(res, i^2 + 1) ) ); q = #res; forstep(i = 3, logint(n, 2), 2, for(j = 1, q, c = res[j]^i; if(c <= n, listput(res, c) , next(2) ) ) ); listsort(res); res } \\ David A. Corneth, Mar 17 2019

A000010(a(n)) = (q^(2k))*(q-1) and A051953(a(n)) = q^(2k), where q = 1 + x^2 and is prime.

A078165 Numbers k such that phi(k) is a perfect 5th power.

Original entry on oeis.org

1, 2, 51, 64, 68, 80, 96, 102, 120, 1285, 2048, 2056, 2176, 2560, 2570, 2720, 3072, 3084, 3264, 3840, 4080, 7957, 8227, 8279, 9079, 9139, 9709, 9919, 10355, 10595, 11667, 11673, 11691, 12099, 12393, 12483, 12753, 12987, 13797, 14715, 14763

Offset: 1

Labos Elemer, Nov 27 2002

nonn

As phi(2^(5*n+1)) = (2^n)^5, A013822 is a subsequence. - Bernard Schott, Sep 26 2022

Numbers of the form u = 2^(5*k)*3^(5*m + 1), k>=1, m>=0, are terms because phi(u) = 2^(5*k)*3^(5*m) = (2^k*3^m)^5. - Marius A. Burtea, Sep 26 2022

			phi of the sequence includes 1, 32, 1024, 7776, ...; powers arise several times; a(3) = A053576(5) = 51.

Amiram Eldar, Table of n, a(n) for n = 1..10000

A013822 is a subsequence.

Cf. A039770 (square), A039771 (cube), A078164 (4th), A078165 (5th, this sequence), A078166 (6th), A078167 (7th), A078168 (8th), A078169 (9th), A078170 (10th power), A001317, A053576, A045544, A000010.

k=5; Do[s=EulerPhi[n]^(1/k); If[IntegerQ[s], Print[n]], {n, 1, 5000}]
Select[Range[15000],IntegerQ[Surd[EulerPhi[#],5]]&] (* Harvey P. Dale, Jul 26 2019 *)

is(n)=ispower(eulerphi(n),5) \\ Charles R Greathouse IV, Apr 24 2020

A078166 Numbers k such that phi(k) is a perfect sixth power.

Original entry on oeis.org

1, 2, 85, 128, 136, 160, 170, 192, 204, 240, 4369, 8192, 8224, 8704, 8738, 10240, 10280, 10880, 12288, 12336, 13056, 15360, 15420, 16320, 47197, 47239, 47989, 49267, 49589, 50557, 51319, 52429, 52649, 55699, 57589, 57953, 59495, 63973

Offset: 1

Labos Elemer, Nov 27 2002

nonn

As phi(2^(6*n+1)) = (2^n)^6, A277757 is a subsequence. - Bernard Schott, Sep 23 2022

			phi of the sequence includes 1, 64, 4096, 46656,..; powers arise several times; a(3)= A053576(6) = 85; in sequence relatively large jumps are observable when power of new numbers appear.

Amiram Eldar, Table of n, a(n) for n = 1..10000

A277757 is a subsequence.
Numbers k such that phi(k) is a perfect power: A039770 (square), A039771 (cube), A078164 (4th), A078165 (5th), A078166 (6th, this sequence), A078167 (7th), A078168 (8th), A078169 (9th), A078170 (10th power).
Cf. A001317, A053576, A045544, A000010.

k=6; Select[Range[65000],IntegerQ[EulerPhi[#]^(1/k)]&]  (* Harvey P. Dale, Feb 20 2011 *)

is(n)=ispower(eulerphi(n),6) \\ Charles R Greathouse IV, Apr 24 2020

A078167 Numbers k such that phi(k) is a perfect 7th power.

Original entry on oeis.org

1, 2, 255, 256, 272, 320, 340, 384, 408, 480, 510, 21845, 32768, 32896, 34816, 34952, 40960, 41120, 43520, 43690, 49152, 49344, 52224, 52428, 61440, 61680, 65280, 280999, 281587, 282637, 282949, 283897, 294409, 297449, 300409, 302039, 304399

Offset: 1

Labos Elemer, Nov 27 2002

nonn

			phi of the sequence includes 1, 128, 16384, 279936, etc..; powers arise several times; a(3) = A053576(7) = 255; in sequence rather large jumps arise when power of new numbers appear.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A039770 (square), A039771 (cube), A078164 (4th), A078165 (5th), A078166 (6th), A078167 (7th, this sequence), A078168 (8th), A078169 (9th), A078170 (10th power), A001317, A053576, A045544, A000010.

k=7; Do[s=EulerPhi[n]^(1/k); If[IntegerQ[s], Print[n]], {n, 1, 1000000}]

is(n)=ispower(eulerphi(n),7) \\ Charles R Greathouse IV, Apr 24 2020

A078168 Numbers k such that phi(k) is a perfect 8th power.

Original entry on oeis.org

1, 2, 257, 512, 514, 544, 640, 680, 768, 816, 960, 1020, 65537, 131072, 131074, 131584, 139264, 139808, 163840, 164480, 174080, 174760, 196608, 197376, 208896, 209712, 245760, 246720, 261120, 262140, 1682227, 1683109, 1683559, 1683937

Offset: 1

Labos Elemer, Nov 27 2002

nonn

			phi of the sequence includes 1, 256, 65536, 1679616, etc.; powers arise several times; a(3) = A053576(7) = 257; in sequence smoother ranges and quite large jumps arise when power of new numbers appear as phi-values.

Amiram Eldar, Table of n, a(n) for n = 1..7500

Cf. A039770 (square), A039771 (cube), A078164 (4th), A078165 (5th), A078166 (6th), A078167 (7th), A078168 (8th, this sequence), A078169 (9th), A078170 (10th power), A001317, A053576, A045544, A000010.

k=8; Do[s=EulerPhi[n]^(1/k); If[IntegerQ[s], Print[n]], {n, 1, 10000000}]
Select[Range[2*10^6],IntegerQ[Surd[EulerPhi[#],8]]&] (* Harvey P. Dale, Oct 20 2014 *)

is(n)=ispower(eulerphi(n),8) \\ Charles R Greathouse IV, Apr 24 2020

cp's OEIS Frontend

A062732 Squares arising in A039770.

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A002496 Primes of the form k^2 + 1.

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A037896 Primes of the form k^4 + 1.

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A078164 Numbers k such that phi(k) is a perfect biquadrate.

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A039771 Numbers k such that phi(k) is a perfect cube.

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A054755 Odd powers of primes of the form q = x^2 + 1 (A002496).

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