A280986 Least k > 0 such that (k*n)^2 is in A002202, or 0 if no such k exists.

1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 6, 1, 2, 2, 8, 1, 2, 1, 2, 1, 4, 1, 4, 1, 2, 2, 2, 1, 2, 3, 4, 1, 6, 1, 10, 1, 2, 4, 2, 1, 4, 1, 4, 1, 8, 1, 2, 1, 2, 2, 4, 1, 12, 2, 2, 1, 2, 1, 2, 1, 4, 1, 4, 1, 2, 1, 2, 3, 4, 2, 6, 1, 2, 3, 8, 1, 2, 5, 2, 1, 6, 1, 4, 2, 2, 1, 4, 1, 8, 2, 2, 1

Offset: 1

Author

Altug Alkan, Jan 12 2017

Keywords

• nonn

Comments

Pollack and Pomerance showed that almost all squares are missing from the range of Euler's totient function.

Examples

			a(11) = 4 because (k*11)^2 is not in A002202 for 0 < k < 4 and (4*11)^2 is in A002202.
a(95911) = 56 because (k*95911)^2 is not in A002202 for 0 < k < 56 and (56*95911)^2 is in A002202.
		

Links

• P. Pollack and C. Pomerance, Square values of Euler's function

Crossrefs

Cf. A000010, A002202, A039770, A062732, A280988.

Programs

PARI

a(n) = {my(k = 1); while (!istotient((k*n)^2), k++); k; }