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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
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 (list; graph; refs; listen; history; text; internal format)
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 A304807

Adjacent sequences:  A226950 A226951 A226952 * A226954 A226955 A226956

KEYWORD

easy,nonn

AUTHOR

Jean-Fran├žois Alcover, Jun 24 2013

STATUS

approved

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Last modified June 12 19:06 EDT 2021. Contains 344959 sequences. (Running on oeis4.)