A173334 Numbers k such that tau(phi(k)) = phi(sum-of-prime-divisors(k)).

2, 3, 15, 18, 24, 28, 30, 33, 39, 50, 52, 55, 80, 132, 133, 152, 169, 186, 187, 190, 195, 207, 215, 217, 222, 230, 238, 247, 261, 266, 305, 319, 333, 340, 352, 369, 371, 414, 481, 484, 494, 496, 497, 506, 516, 522, 559, 574, 580, 611, 644, 646, 660, 671, 689

Offset

1,1

Comments

Numbers k such that A000005(A000010(k)) = A000010(A008472(k)).

References

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

P. A. MacMahon, Divisors of numbers and their continuations in the theory of partitions, Proc. London Math. Soc., 19 (1921), 75-113.

W. Sierpinski, Number Of Divisors And Their Sum, Monogr. Matemat. 42 (1964) chapter IV

Wikipedia, Euler's totient function

Formula

{n : A062821(n)= phi(A008472(n))}.

Example

For n=15, tau(phi(15)) = tau(8)=4 equals phi(A008472(15))=phi(8) = 4, which adds 15 to the sequence.
For n=18, tau(phi(18)) = tau(6) =4 equals phi(A008472(18)) = phi(5) = 4, which adds 18 to the sequence.

Maple

with(numtheory): for n from 1 to 1800 do : t1:= ifactors(n)[2] : t2 :=sum(t1[i][1], i=1..nops(t1)):if tau(phi(n)) = phi(t2) then print (n): else fi : od :

Mathematica

Select[Range[2, 700], DivisorSigma[0, EulerPhi[#]] == EulerPhi[Total[FactorInteger[#][[All, 1]]]] &]
(* Jean-François Alcover, May 19 2011 *)

Prog

(Magma) [m:m in [2..700]|#Divisors(EulerPhi(m)) eq EulerPhi(&+PrimeDivisors(m))]; // Marius A. Burtea, Jul 10 2019
(PARI) isok(n) = numdiv(eulerphi(n)) == eulerphi(vecsum(factor(n)[, 1])); \\ Michel Marcus, Jul 10 2019

Crossrefs

Cf. A000005, A000010, A008472, A062821.

Sequence in context: A066491 A282383 A299486 * A331089 A294131 A274003

Adjacent sequences: A173331 A173332 A173333 * A173335 A173336 A173337

Keyword

nonn

Author

Michel Lagneau, Feb 16 2010

Extensions

Removed sopf acronym. Updated references and links - R. J. Mathar, Mar 10 2010

Status

approved