A064447 -id:A064447 - cp's OEIS frontend

A366821 a(n) is phi(n^n-1) where phi is the Euler totient function.

2, 12, 128, 1400, 30240, 264992, 6635520, 141087744, 5890320000, 114117380608, 4662793175040, 99053063903040, 5470524984113280, 167080949856000000, 9208981628670443520, 413582117375670921216, 29531731481729468006400, 659473218553437863041320

Offset: 2

Sean A. Irvine, Oct 24 2023

nonn

Amiram Eldar, Table of n, a(n) for n = 2..138 (terms 2..102 from Robert G. Wilson v)

Cf. A000010, A048861, A064447, A309941, A334167, A344870, A366819, A366822.

a:= n-> numtheory[phi](n^n-1):
seq(a(n), n=2..20);  # Alois P. Heinz, Oct 26 2023

Array[EulerPhi[#^# - 1] &, 18, 2] (* Michael De Vlieger, Oct 24 2023 *)

PARI
```
a(n) = eulerphi(n^n-1);
```

a(n) = A000010(A048861(n)).

A366822 a(n) is phi(n^n + 1) where phi is the Euler totient function.

Original entry on oeis.org

1, 1, 4, 12, 256, 1040, 41472, 407680, 16515072, 152845056, 9897840000, 89493288192, 8732596764672, 129785922489600, 10576701872701440, 210729768933600000, 18446676793287966720, 275746753962112254720, 28084363369373740400640, 791359800910482004224000

Offset: 0

Sean A. Irvine, Oct 24 2023

nonn

Robert G. Wilson v, Table of n, a(n) for n = 0..72
Eric Weisstein's World of Mathematics, Sierpinski Number of the First Kind

Cf. A000010, A014566, A064447, A366821.

{1}~Join~Array[EulerPhi[#^# + 1] &, 19] (* Michael De Vlieger, Oct 24 2023 *)

PARI
```
a(n) = eulerphi(n^n+1);
```

a(n) = A000010(A014566(n)).

A276035 Least k such that n divides phi(k^k) (k > 0).

Original entry on oeis.org

1, 2, 3, 4, 5, 3, 7, 4, 3, 5, 11, 6, 13, 7, 15, 4, 17, 3, 19, 5, 7, 11, 23, 6, 5, 13, 6, 14, 29, 15, 31, 4, 33, 17, 35, 6, 37, 19, 13, 10, 41, 7, 43, 22, 15, 23, 47, 6, 7, 5, 51, 13, 53, 6, 11, 14, 19, 29, 59, 15, 61, 31, 21, 4, 65, 33, 67, 17, 69, 35

Offset: 1

Altug Alkan, Aug 16 2016

nonn

The first term that has 3 prime divisors is a(240) = 2*3*5.

			a(9) = 3 because 9 divides phi(3^3) = 18.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A064447.

a(n)=my(k = 1); while(eulerphi(k^k) % n, k++); k;

a(n)=my(k=1); while(eulerphi(k)*Mod(k,n)^(k-1), k++); k \\ Charles R Greathouse IV, Aug 16 2016

(log n)/W(log n) < a(n) <= n for n > 1. - Charles R Greathouse IV, Aug 16 2016

A276040 Least k such that n^n divides phi(k^k) (k > 0).

Original entry on oeis.org

1, 4, 6, 8, 10, 12, 14, 12, 18, 20, 22, 24, 26, 28, 30, 24, 34, 36, 38, 40, 42, 44, 46, 36, 50, 52, 45, 56, 58, 60, 62, 48, 66, 68, 70, 72, 74, 76, 78, 60, 82, 84, 86, 88, 90, 92, 94, 72, 98, 100, 102, 104, 106, 90, 110, 84, 114, 116, 118, 120

Offset: 1

Altug Alkan, Aug 17 2016

nonn

Indices of odd terms in this sequence are 1, 27, 81, 135, 189, 297, 343, 351, 405, 459, 513, 621, 625, 675, 783, ...

			a(3) = 6 because 3^3 divides phi(6^6) = 15552.

Cf. A064447.

Table[k = 1; While[! Divisible[EulerPhi[k^k], n^n], k++]; k, {n, 60}] (* Michael De Vlieger, Aug 21 2016 *)

a(n) = {my(k = 1); while(eulerphi(k^k) % n^n, k++); k; }

cp's OEIS Frontend

A366821 a(n) is phi(n^n-1) where phi is the Euler totient function.

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A366822 a(n) is phi(n^n + 1) where phi is the Euler totient function.

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Mathematica

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A276035 Least k such that n divides phi(k^k) (k > 0).

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PARI

PARI

Formula

A276040 Least k such that n^n divides phi(k^k) (k > 0).

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Author

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Comments

Examples

Crossrefs

Programs

Mathematica

PARI