%I #13 Mar 19 2021 07:00:43

%S 1,2,4,6,12,18,24,30,48,60,78,90,120,150,180,210,330,360,390,420,630,

%T 840,1050,1260,1470,1680,1890,2100,2310,3360,3570,3990,4200,4620,5460,

%U 6300,6930,9240,10710,10920,11550,13860,16380,17220,17850,18480,20790,27720,30030,39270

%N Indices of records of A007015.

%C Numbers m such that the smallest solution k to the equation phi(m+k) = phi(k) is larger than all the corresponding smallest solutions for all numbers below m.

%C The corresponding record values are 1, 4, 8, 24, 48, 52, 96, ... (see the link for more values).

%C Apparently, a(n) is even for n > 1, divisible by 6 for n > 3, by 30 for n > 9, and by 210 for n > 19. These observations are based on data up to n=100.

%C It seems that in general, for all k >= 1 there is a number n_k such that all the terms a(n) with n > n_k are divisible by the first k primes.

%C Furthermore, it seems that all the terms are of the form m*p^e, were m is a term of A055932, and p^e is a prime power (A000961).

%H Amiram Eldar, <a href="/A342702/b342702.txt">Table of n, a(n) for n = 1..100</a>

%H Amiram Eldar, <a href="/A342702/a342702.txt">Table of n, a(n), A007015(a(n)) for n = 1..100</a>

%e The first 6 terms of A007015 are 1, 4, 3, 8, 5 and 24. The record values, 1, 4, 8 and 24 occur at 1, 2, 4 and 6, the first 4 terms of this sequence.

%t f[n_] := Module[{k = 1}, While[EulerPhi[n + k] != EulerPhi[k], k++]; k]; fm =0; s = {}; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, n]];, {n, 1, 1000}]; s

%Y Cf. A000961, A007015, A055932.

%K nonn

%O 1,2

%A _Amiram Eldar_, Mar 18 2021