A076245 -id:A076245 - cp's OEIS frontend

A051547 a(n) = lcm{ phi(1), ..., phi(n) }, where phi is Euler's totient function A000010.

1, 1, 2, 2, 4, 4, 12, 12, 12, 12, 60, 60, 60, 60, 120, 120, 240, 240, 720, 720, 720, 720, 7920, 7920, 7920, 7920, 7920, 7920, 55440, 55440, 55440, 55440, 55440, 55440, 55440, 55440, 55440, 55440, 55440, 55440, 55440, 55440, 55440, 55440, 55440, 55440, 1275120, 1275120, 1275120

Offset: 1

N. J. A. Sloane

nonn

Michael De Vlieger, Table of n, a(n) for n = 1..10000
P. Moree, H. Roskam, On an arithmetical function related to Euler's totient and the discriminator, Fib. Quart. 33 (1995) 332-340.

Cf. A000010, A076244 (distinct values), A076245 (n where a(n) > a(n-1)).

FoldList[LCM @@ {#1, EulerPhi@ #2} &, Range@ 44] (* Michael De Vlieger, Dec 09 2018 *)

a(n) = lcm(vector(n, k, eulerphi(k))); \\ Michel Marcus, Jul 30 2017

apply( A051547(n)=lcm(apply(eulerphi,[2..n])), [1..50]) \\ Defines the function A051547; apply(...) for check & example. - M. F. Hasler, Dec 09 2018

A378640 Smallest m such that phi(m) does not divide n, where phi is the Euler totient function (A000010).

Original entry on oeis.org

3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 15, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5

Offset: 1

Paolo Xausa, Dec 05 2024

Up to n = 10^7 the distinct terms of the sequence (which are also the record values) are {3, 5, 7, 11, 15, 17, 19, 23, 29, 47, 51, 53}. Is this A076245 (for n >= 2)?
First differs from A095366 at n = 60.
It appears that a(n) = A095366(n) except when n = 60*(2*k + 1), with k >= 0, where a(n) = 15 while A095366(n) = 17.

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A000010, A076245, A095366, A378638, A378641, A378642.

A378640[n_] := If[OddQ[n], 3, Module[{m = 4}, While[Divisible[n, EulerPhi[++m]]]; m]];
Array[A378640, 100]

a(n) = 3 if n is odd.

A076246 Totients of those numbers at which values of A051547 increase: in these consecutive terms new prime powers arise, i.e., which did not occur in neither of preceding terms.

Original entry on oeis.org

2, 4, 6, 10, 8, 16, 18, 22, 28, 46, 32, 52, 58, 54, 82, 64, 100, 102, 106, 148, 162, 166, 172, 178, 190, 196, 226, 250, 128, 256, 262, 268, 282, 292, 310, 316, 346, 358, 366, 382, 388, 466, 478, 486, 502, 508, 556, 562, 568, 586, 606, 618, 642, 652, 676, 708

Offset: 1

Labos Elemer, Oct 08 2002

nonn

			8 = 2*2*2 immediately follows 10 = 2*5; 58 = 2*29 follows 52 = 2*2*13. In both cases, the latter term has a new prime factor (like 29) or an old one at a higher power (like 2*2*2).

Cf. A003418, A051451, A051547, A076244, A076245.

s0=1; s1=1; Do[s0=s1; s1=LCM[s1, EulerPhi[n]]; If[ !Equal[s0, s1], Print[n]], {n, 1, 1000}]

lista(nn) = {least = 1; for (n=2, nn, nleast = lcm(least, eulerphi(n)); if (nleast > least, print1(eulerphi(n), ", ")); least = nleast;);} \\ Michel Marcus, Jul 30 2017

a(n) = phi(A076245(n + 1)). - Sean A. Irvine, Mar 25 2025

cp's OEIS Frontend

A051547 a(n) = lcm{ phi(1), ..., phi(n) }, where phi is Euler's totient function A000010.

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A378640 Smallest m such that phi(m) does not divide n, where phi is the Euler totient function (A000010).

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A076246 Totients of those numbers at which values of A051547 increase: in these consecutive terms new prime powers arise, i.e., which did not occur in neither of preceding terms.

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