New sequence derived from the totient function

[Benoît Jubin]

Dear SeqFans,

I'm contemplating adding the following sequence, derived from the
Euler totient function:

a(n) is the least m such that k>=m implies phi(k)>=n

It is easily derived from the two sequences A002202 (increasing
sequence of values of phi) and A006511 (a(n) is the largest x such
that phi(x)=m, where m=A002202(n)), by the following construction:

for any increasing sequence A and any sequence B, form the sequence C
by setting C(n)=B(k+1) where k is the unique integer such that
A(k)<n<=A(k+1). Then define D by D(0)=C(0) (or D(1)=C(1)) and
D(n+1)=max(D(n),C(n+1)).

- Does this transformation have a name ?
- Is it worth adding this sequence ?
- Which comments should be entered in the OEIS ? (my original
motivation for this sequence is that it is a lower bound of A137315)
- Is it equivalent to c.n.ln(ln(n)) ? with which c ?

Thank you,
Benoit