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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.
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%I #8 Jul 17 2013 07:17:59

%S 1,2,9,14,15,18,20,22,46,94,118,166,214,231,248,286,308,310,334,344,

%T 350,351,358,366,372,392,399,405,406,430,454,483,490,494,516,518,522,

%U 526,532,536,568,595,598,632,638,644,654,663,666

%N 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.

%C 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.

%H Vincenzo Librandi, <a href="/A226953/b226953.txt">Table of n, a(n) for n = 1..1000</a>

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

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

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

%K easy,nonn

%O 1,2

%A _Jean-François Alcover_, Jun 24 2013