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 A291549 Numbers n such that both phi(n) and psi(n) are perfect squares. 2
 1, 60, 170, 240, 315, 540, 679, 680, 960, 1500, 2142, 2160, 2720, 2835, 3840, 4250, 4365, 4860, 5770, 6000, 7875, 8568, 8640, 9154, 9809, 10880, 13500, 14322, 15360, 15435, 17000, 19278, 19440, 22413, 23080, 24000, 25515, 29682, 33271, 34272, 34560, 36616, 37114, 37500 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Intersection of A039770 and A291167. Squarefree terms are 1, 170, 679, 5770, 9154, 9809, 14322, ... From Robert Israel, May 16 2019: (Start) If n is in the sequence and p is a prime factor of n then p^2*n is in the sequence. If n and m are coprime members of the sequence, then n*m is in the sequence. (End) LINKS Robert Israel, Table of n, a(n) for n = 1..2000 EXAMPLE 60 is a term because phi(60) = 16 and psi(60) = 144 are both perfect squares. MAPLE filter:= proc(n) local F, psi, phi, p;    F:= numtheory:-factorset(n);    issqr( n*mul(1-1/p, p=F)) and issqr(n*mul(1+1/p, p=F)) end proc: select(filter, [\$1..50000]); # Robert Israel, May 15 2019 MATHEMATICA Select[Range[10^5], AllTrue[{EulerPhi@ #, If[# < 1, 0, # Sum[MoebiusMu[d]^2/d, {d, Divisors@ #}]]}, IntegerQ@ Sqrt@ # &] &] (* Michael De Vlieger, Aug 26 2017, after Michael Somos at A001615 *) PROG (PARI) a001615(n) = my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1)) isok(n) = issquare(eulerphi(n)) && issquare(a001615(n)); \\ after Charles R Greathouse IV at A001615 CROSSREFS Cf. A000010, A000290, A001615, A039770, A291167. Sequence in context: A119630 A216480 A257146 * A259946 A249911 A292223 Adjacent sequences:  A291546 A291547 A291548 * A291550 A291551 A291552 KEYWORD nonn,easy AUTHOR Amiram Eldar and Altug Alkan, Aug 26 2017 STATUS approved

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Last modified September 28 17:43 EDT 2020. Contains 337393 sequences. (Running on oeis4.)