A339883 - OEIS

%I #16 Jan 11 2022 06:03:43

%S 24,72,25440,33840,38880,48960,99360,123120,208320,458640,510720,

%T 519360,532800,583440,596400,622080,663840,838800,846960,873600,

%U 893760,942480,1050480,1065600,1078800,1163040,1201200,1327200,1408320,1419840,1567440,1734000,1809600

%N Values of Euler's totient phi for A050498.

%C For the shown values the arithmetic progression with difference 6 has exactly 4 terms. Conjecture 1: this holds for all A050498 entries.

%C Conjecture 2: All a(n) are divisible by 24, starting with [1, 3, 1060, 1410, 1620, 2040, 4140, 5130, 8680, 19110, 21280, 21640, 22200, 24310, 24850, 25920, 27660, 34950, 35290, 36400, 37240, 39270, 43770, 44400, 44950, 48460, ...].

%C In the Lal and Gillard link only the first three A050498 values (with n <= 10^5) and their corresponding phi values are given.

%D David Wells, Curious and interesting numbers, Penguin Books, Revised edition, 1997 p. 112. [Gives under the number 72 the first three values of A050498 but with 76236 instead of 76326]

%H Amiram Eldar, <a href="/A339883/b339883.txt">Table of n, a(n) for n = 1..10000</a>

%H M. Lal and P. Gillard, <a href="https://doi.org/10.1090/S0025-5718-1974-0341814-9">On the Equation phi(n) = phi(n+k)</a>, Mathematics of Computation, Volume 26, Number 118 (1972) 579-584. [Eq. (4), Table 3, for k = 6, n <= 10^5]

%F a(n) = A000010(A050498(n)), n >= 1.

%Y Cf. A000010, A050498, A163573.

%K nonn

%O 1,1

%A _Wolfdieter Lang_, Jan 09 2021