A210501 Number of odd solutions to phi(k) = prime(n) - 1.

1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3, 3, 2, 1, 1, 1, 4, 1, 1, 6, 1, 1, 2, 4, 2, 1, 1, 4, 2, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 5, 1, 4, 1, 1, 1, 1, 1, 1, 2, 1, 10, 1, 1, 1, 1, 1, 4, 3, 1, 1, 1, 1, 6, 1, 1, 5, 1, 3, 3, 1, 1, 1, 1, 1, 1, 6, 4, 2, 1, 6, 1, 11, 1, 1, 3

Offset: 1

Author

Arkadiusz Wesolowski, Jan 19 2013

Keywords

• nonn

Comments

a(n) <= A210500(n).

Examples

			The set {k: phi(k) = 12} is {13, 21, 26, 28, 36, 42}. Thus, if phi(k) = prime(6) - 1, the equation has exactly two odd solutions. Hence, a(6) = 2.
		

References

• Alexander S. Karpenko, Lukasiewicz's Logics and Prime Numbers, Luniver Press, Beckington, 2006, pp. 52-56.

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010, A032446, A058339, A210500, A210502.

Programs

Mathematica

r = 87; lst1 = Table[EulerPhi[n], {n, (Prime[r] - 1)^2 + 1}]; lst2 = {}; Do[p = Prime[n]; AppendTo[lst2, Length@Select[Flatten@Position[Take[lst1, {p - 1, (p - 1)^2 + 1}], Prime[n] - 1], EvenQ]], {n, r}]; lst2

Formula

a(n) = A058339(n) - A210500(n).