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

1,2

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.

Links

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A220249 A071343 A043401 * A274133 A288483 A353308

Adjacent sequences: A226950 A226951 A226952 * A226954 A226955 A226956

Keyword

easy,nonn

Author

Jean-François Alcover, Jun 24 2013

Status

approved