cp's OEIS Frontend

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)

Numbers k such that tau(k) divides phi(k) are in A020491.

Only for seven integers which are in A020488, we have a(n) = 1.

The integers such that a(n) = 2, 3, 4 are respectively in A062516, A063469, A063470.

When p is an odd prime then phi(p) = p-1, tau(p) = 2, so phi(p)/tau(p) = (p-1)/2 and A005097 is an infinite subsequence.

For k = A058891(m+1), that is 2^A000225(m), with m>=2, the corresponding quotient phi(k)/tau(k) is the integer A076688(m). - Bernard Schott, Aug 15 2020