A226953 Leap year numbers: numbers n such that tau(phi(n)) = phi(tau(n))^2, where tau(n) is the number of divisors of n and phi(n) the Euler totient function.

1, 2, 9, 14, 15, 18, 20, 22, 46, 94, 118, 166, 214, 231, 248, 286, 308, 310, 334, 344, 350, 351, 358, 366, 372, 392, 399, 405, 406, 430, 454, 483, 490, 494, 516, 518, 522, 526, 532, 536, 568, 595, 598, 632, 638, 644, 654, 663, 666

Offset: 1

Author

Jean-François Alcover, Jun 24 2013

Keywords

• easy
• nonn

Comments

Paraphrasing Doug Iannucci, n is called a "leap year number" if tau(phi(n)) = phi(tau(n))^2 (366 is a leap year number, hence the sequence name). The beast number is a leap year number. The only prime leap year number is 2.

Examples

			phi(666)=216, tau(216)=16, tau(666)=12, phi(12)=4, 4^2=16, therefore 666 is in the sequence.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A137815 (Doug Iannucci's "year numbers").

Programs

Mathematica

Select[Range[1000], DivisorSigma[0, EulerPhi[#]] == EulerPhi[DivisorSigma[0, #]]^2 &]