A366671 -id:A366671 - cp's OEIS frontend

A366655 Number of distinct prime divisors of 8^n + 1.

1, 1, 2, 2, 2, 3, 4, 3, 3, 3, 5, 4, 4, 3, 6, 5, 3, 5, 6, 4, 4, 5, 6, 4, 5, 6, 9, 6, 5, 4, 10, 4, 3, 7, 9, 10, 6, 6, 8, 5, 6, 6, 10, 5, 7, 9, 8, 6, 7, 6, 12, 9, 5, 5, 10, 10, 8, 6, 8, 7, 8, 3, 9, 10, 4, 10, 12, 7, 8, 6, 14, 7, 8, 5, 10, 10, 8, 11, 16, 5, 7, 10

Offset: 0

Sean A. Irvine, Oct 15 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 0..502

Cf. A062395, A001221, A057936, A274905, A366651, A366632, A366656, A366657, A366658, A366671.

Cf. A046799, A366580, A366605, A366615, A366627, A366636, A366664, A119704, A366686, A366712.

for(n = 0, 100, print1(omega(8^n + 1), ", "))

a(n) = omega(8^n+1) = A001221(A062395(n)).

a(n) = A046799(3*n). - Max Alekseyev, Jan 09 2024

A366658 a(n) = phi(8^n+1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

1, 6, 48, 324, 3840, 19800, 186624, 1365336, 16515072, 84768120, 760320000, 5632621632, 64258375680, 366369658200, 3105655160832, 20140520400000, 280012271910912, 1495522910085120, 12824556668190720, 95907982079387520, 1080582572777472000, 5688765822212629632

Offset: 0

Sean A. Irvine, Oct 15 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 0..502

Cf. A062395, A000010, A057936, A274905, A366654, A366655, A366656, A366657, A366671.

Cf. A053285, A366579, A366608, A366618, A366630, A366639, A366667, A366669, A366690, A366716.

EulerPhi[8^Range[0, 21] + 1] (* Paul F. Marrero Romero, Oct 17 2023 *)

PARI
```
{a(n) = eulerphi(8^n+1)}
```

from sympy import totient
def A366658(n): return totient((1<<3*n)+1) # Chai Wah Wu, Oct 15 2023

a(n) = A000010(A062395(n)). - Paul F. Marrero Romero, Nov 06 2023

a(n) = A053285(3*n). - Max Alekseyev, Jan 09 2024

A366609 Smallest prime dividing 4^n + 1.

Original entry on oeis.org

2, 5, 17, 5, 257, 5, 17, 5, 65537, 5, 17, 5, 97, 5, 17, 5, 641, 5, 17, 5, 257, 5, 17, 5, 193, 5, 17, 5, 257, 5, 17, 5, 274177, 5, 17, 5, 97, 5, 17, 5, 65537, 5, 17, 5, 257, 5, 17, 5, 641, 5, 17, 5, 257, 5, 17, 5, 449, 5, 17, 5, 97, 5, 17, 5, 59649589127497217

Offset: 0

Sean A. Irvine, Oct 14 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 0..1983

Bisection of A002586.

Cf. A002586, A038371, A052539, A074476, A274903, A366605, A366606, A366607, A366608, A366670, A366671, A366719.

A366670 Smallest prime dividing 6^n + 1.

Original entry on oeis.org

2, 7, 37, 7, 1297, 7, 13, 7, 17, 7, 37, 7, 1297, 7, 37, 7, 353, 7, 13, 7, 41, 7, 37, 7, 17, 7, 37, 7, 281, 7, 13, 7, 2753, 7, 37, 7, 577, 7, 37, 7, 17, 7, 13, 7, 89, 7, 37, 7, 193, 7, 37, 7, 1297, 7, 13, 7, 17, 7, 37, 7, 41, 7, 37, 7, 4926056449, 7, 13, 7, 137

Offset: 0

Sean A. Irvine, Oct 15 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 0..4095

Cf. A020639, A062394, A274904, A366630.

Cf. A002586, A366609, A366671, A038371, A366719.

Table[FactorInteger[6^n + 1][[1,1]], {n, 0, 68}] (* Paul F. Marrero Romero, Oct 17 2023 *)

a(n) = A020639(A062394(n)). - Paul F. Marrero Romero, Oct 17 2023

cp's OEIS Frontend

A366655 Number of distinct prime divisors of 8^n + 1.

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A366658 a(n) = phi(8^n+1), where phi is Euler's totient function (A000010).

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A366609 Smallest prime dividing 4^n + 1.

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A366670 Smallest prime dividing 6^n + 1.

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