

A280196


Numbers n such that a^(n1) == 1 (mod n^2) has no solutions with 1 < a < n^21.


2



1, 2, 3, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 27, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 54, 56, 58, 60, 62, 64, 68, 72, 74, 78, 80, 81, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 114, 116, 118, 120, 122, 126, 128, 132, 134, 136, 138
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OFFSET

1,2


COMMENTS

1 and numbers n such that A185103(n) = n^2 + (1)^n.


LINKS



EXAMPLE

a(4) = 4 is in the sequence because a^3 == 1 (mod 4^2) has no solutions except a == 1 (mod 4^2).
a(7) = 9 is in the sequence because a^8 == 1 (mod 9^2) has no solutions except a == 1 (mod 9^2) and a == 80 (mod 9^2), and 80 = 9^21.


MAPLE

Aeven:= select(t > igcd(t1, numtheory:phi(t^2))=1, {seq(i, i=2..1000, 2}}):
Aodd:= {seq(3^i, i=0..floor(log[3](1000)))}:
sort(convert(Aeven union Aodd, list));


MATHEMATICA

Aeven = Select[Range[2, 1000, 2], GCD[#1, EulerPhi[#^2]] == 1&];
Aodd = 3^Range[0, Floor[Log[3, 1000]]];


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



