A076244 -id:A076244 - 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

A076245 Positions of records in A051547.

Original entry on oeis.org

1, 3, 5, 7, 11, 15, 17, 19, 23, 29, 47, 51, 53, 59, 81, 83, 85, 101, 103, 107, 149, 163, 167, 173, 179, 191, 197, 227, 251, 255, 257, 263, 269, 283, 293, 311, 317, 347, 359, 367, 383, 389, 467, 479, 487, 503, 509, 557, 563, 569, 587, 607, 619, 643, 653, 677

Offset: 1

Labos Elemer, Oct 08 2002

nonn

Observe that both primes and composites (including 15, 51, 81, 85, and 255) occur.

In totients of consecutive terms some prime-factor appears at higher power than in preceding ones: see A076246 and A051451.

Michael De Vlieger, Table of n, a(n) for n = 1..13256 (First 1924 terms from _Vincenzo Librandi_; a(n) <= 10^6.)

Cf. A003418, A051451, A051547, A076244.

With[{s = FoldList[LCM @@ {#1, EulerPhi@ #2} &, Range[700]]}, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* Michael De Vlieger, Dec 09 2018 *)

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

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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A076245 Positions of records in A051547.

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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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