A105261 Values of n such that phi(n)=c(n)^2, where phi is the Euler totient function and c(n) is the product of the distinct prime factors of n (c(1)=1).

1, 8, 108, 250, 6174, 41154

Offset

1,2

Comments

This sequence has exactly six terms (see the Monthly reference). phi(n)=A000010(n); c(n)=A007947(n).

References

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 108, p. 38, Ellipses, Paris 2008.

J.-M. De Koninck & A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 745 ; pp 95; 317-8, Ellipses Paris 2004.

J.-M. De Koninck & A. Mercier, 1001 Problems in Classical Number Theory, Problem 745 ; pp 80; 273-4, Amer. Math. Soc. Providence RI 2007.

Links

Table of n, a(n) for n=1..6.

J.-M. De Koninck, When the Totient Is the Product of the Squared Prime Divisors: Problem 10966, Amer. Math. Monthly, 111 (2004), p. 536.

Example

8 is in the sequence because phi(8)=4 (1,3,5,7), c(8)=2 (2 being the only prime divisor of 8) and so phi(8)=c(8)^2.

Maple

with(numtheory): c:=proc(n) local div: div:=convert(factorset(n), list): product(div[j], j=1..nops(div)) end:p:=proc(n) if phi(n)=c(n)^2 then n else fi end: seq(p(n), n=1..42000);

Mathematica

Select[Range[42000], EulerPhi[#] == Times @@ FactorInteger[#][[All, 1]]^2 & ] (* Jean-François Alcover, Sep 12 2011 *)

Crossrefs

Cf. A000010, A007947.

Sequence in context: A365818 A239985 A274892 * A187288 A275134 A187190

Adjacent sequences: A105258 A105259 A105260 * A105262 A105263 A105264

Keyword

fini,nonn,full

Author

Emeric Deutsch, Apr 14 2005

Status

approved