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A280988 Least k such that phi(k*n) is a perfect square, or 0 if no such k exists. 4
1, 1, 4, 2, 1, 2, 9, 1, 7, 1, 41, 1, 21, 9, 4, 2, 1, 6, 3, 2, 3, 41, 89, 2, 5, 14, 4, 13, 113, 2, 143, 1, 25, 1, 9, 3, 1, 2, 7, 1, 11, 3, 49, 25, 7, 89, 1151, 1, 43, 5, 4, 7, 553, 2, 15, 9, 1, 113, 233, 1, 77, 122, 1, 2, 21, 25, 299, 2, 356, 9, 281, 6, 3, 1, 11, 1, 61, 6, 313 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Pollack and Pomerance proved that if phi(a) = b^m, then m = 2 occurs only on a set of density 0.

LINKS

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

Paul Pollack and Carl Pomerance, Square values of Euler's function, Bulletin of the London Mathematical Society, Vol. 46, No. 2 (2014), pp. 403-414, alternative link.

EXAMPLE

a(11) = 41 because phi(k*11) is not a perfect square for 0 < k < 41 and phi(41*11) = 20^2.

MAPLE

f:= proc(n) local k;

    for k from 1 do

      if issqr(numtheory:-phi(k*n)) then return k fi

   od

end proc:

map(f, [$1..100]); # Robert Israel, Jan 12 2017

MATHEMATICA

a[n_] := Module[{k = 1}, While[!IntegerQ[Sqrt[EulerPhi[k*n]]], k++]; k]; Array[a, 80] (* Amiram Eldar, Jul 13 2019 *)

PROG

(PARI) a(n) = {my(k = 1); while (!issquare(eulerphi(k*n)), k++); k; }

CROSSREFS

Cf. A000010, A039770, A062732, A280986.

Sequence in context: A327252 A229974 A281065 * A175665 A200586 A097525

Adjacent sequences:  A280985 A280986 A280987 * A280989 A280990 A280991

KEYWORD

nonn

AUTHOR

Altug Alkan, Jan 12 2017

STATUS

approved

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Last modified June 24 13:42 EDT 2021. Contains 345416 sequences. (Running on oeis4.)