OFFSET
1,2
COMMENTS
In other words, numbers k such that d(k) divides phi(k).
From Enrique Pérez Herrero, Aug 11 2010: (Start)
sigma_0(k) divides phi(k) when:
k is an odd prime: A065091;
k is an odd squarefree number: A056911;
k = 2^m, where m <> 1 is a Mersenne number (A000225).
If d divides (p-1), with p prime, then p^(d-1) is in this sequence, as are p^(p-1), p^(p-2) and p^(-1+p^n).
(End)
phi(n) and d(n) are multiplicative functions, so if m and n are coprime and both of them are in this sequence then m*n is also in this sequence. - Enrique Pérez Herrero, Sep 05 2010
From Bernard Schott, Aug 14 2020: (Start)
The corresponding quotients are in A289585.
About the 3rd case of Enrique Pérez Herrero's comment: if k = 2^M_m, where M_m = 2^m - 1 is a Mersenne number >= 3 (A000225), then the corresponding quotient phi(k)/d(k) is the integer 2^(2^m-m-2) = A076688(m); hence, these numbers k, A058891 \ {2}, form a subsequence. (End)
LINKS
Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000
Psychedelic Geometry Blogspot, Fermat and Mersenne Numbers Conjecture-(2)
MATHEMATICA
Select[ Range[ 105 ], IntegerQ[ EulerPhi[ # ]/DivisorSigma[ 0, # ] ]& ]
PROG
(PARI) isok(k) = !(eulerphi(k) % numdiv(k)); \\ Michel Marcus, Aug 10 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved