[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
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
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
KEYWORD
nonn
AUTHOR
Altug Alkan, Jan 12 2017
STATUS
approved