A339883 Values of Euler's totient phi for A050498.

24, 72, 25440, 33840, 38880, 48960, 99360, 123120, 208320, 458640, 510720, 519360, 532800, 583440, 596400, 622080, 663840, 838800, 846960, 873600, 893760, 942480, 1050480, 1065600, 1078800, 1163040, 1201200, 1327200, 1408320, 1419840, 1567440, 1734000, 1809600

Offset: 1

Author

Wolfdieter Lang, Jan 09 2021

Keywords

• nonn

Comments

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

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, ...].

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

References

• 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]

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• M. Lal and P. Gillard, On the Equation phi(n) = phi(n+k), Mathematics of Computation, Volume 26, Number 118 (1972) 579-584. [Eq. (4), Table 3, for k = 6, n <= 10^5]

Crossrefs

Cf. A000010, A050498, A163573.

Formula

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