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A342702
Indices of records of A007015.
1
1, 2, 4, 6, 12, 18, 24, 30, 48, 60, 78, 90, 120, 150, 180, 210, 330, 360, 390, 420, 630, 840, 1050, 1260, 1470, 1680, 1890, 2100, 2310, 3360, 3570, 3990, 4200, 4620, 5460, 6300, 6930, 9240, 10710, 10920, 11550, 13860, 16380, 17220, 17850, 18480, 20790, 27720, 30030, 39270
OFFSET
1,2
COMMENTS
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.
The corresponding record values are 1, 4, 8, 24, 48, 52, 96, ... (see the link for more values).
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.
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.
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).
EXAMPLE
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.
MATHEMATICA
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Mar 18 2021
STATUS
approved