A179976 -id:A179976 - cp's OEIS frontend

A180060 a(n) = 2^(2^n mod n) mod n.

0, 1, 1, 1, 4, 4, 4, 1, 4, 6, 4, 4, 4, 2, 1, 1, 4, 16, 4, 16, 4, 16, 4, 16, 3, 16, 13, 16, 4, 16, 4, 1, 25, 16, 29, 16, 4, 16, 22, 16, 4, 16, 4, 20, 32, 16, 4, 16, 22, 16, 1, 16, 4, 52, 8, 32, 28, 16, 4, 16, 4, 16, 4, 1, 61, 16, 4, 52, 49, 46, 4, 16, 4, 16, 31, 24, 36, 16, 4, 16

Offset: 1

Juri-Stepan Gerasimov, Jan 14 2011

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000079, A179976.

Table[Mod[2^(Mod[2^n, n]), n], {n, 50}] (* Alonso del Arte, Jan 14 2011 *)
Table[PowerMod[2,PowerMod[2,n,n],n],{n,80}] (* Harvey P. Dale, Oct 09 2019 *)

a(n) = 2^A015910(n) mod n.

Entries corrected by R. J. Mathar, Jan 14 2011

A180061 Numbers k such that (2^(2^k mod k) mod k) = 4.

Original entry on oeis.org

5, 6, 7, 9, 11, 12, 13, 17, 19, 21, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 63, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 133, 137, 139, 149, 151, 157, 163, 167, 172, 173, 179, 181, 190, 191, 193, 196, 197, 199, 211

Offset: 1

Juri-Stepan Gerasimov, Jan 14 2011

nonn

The composite terms in this sequence start 6, 9, 12, 21, 63, 121, 133, 172, 190, 196, ... - R. J. Mathar, Jan 14 2011

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000040, A000079, A179976, A180060.

Select[Range[300],PowerMod[2,PowerMod[2,#,#],#]==4&] (* Harvey P. Dale, Sep 08 2016 *)

s=[]; for(n=1, 1000, if((2^(2^n%n)%n)==4, s=concat(s, n))); s \\ Colin Barker, Jun 27 2014

A180060(a(n)) = 4.

Terms corrected by R. J. Mathar, Jan 14 2011

A180074 Squarefree semiprimes s=p*q, p

Original entry on oeis.org

6, 10, 14, 15, 21, 22, 26, 33, 34, 38, 39, 46, 51, 57, 58, 62, 65, 69, 74, 82, 85, 86, 87, 93, 94, 106, 111, 118, 122, 123, 129, 133, 134, 141, 142, 145, 146, 158, 159, 166, 177, 178, 183, 185, 194, 201, 202, 205, 206, 213, 214, 217, 218, 219, 226, 237

Offset: 1

Juri-Stepan Gerasimov, Jan 14 2011

nonn

It may seem that this is a subsequence of A162730, but it is not so, 131801 being the first counterexample. - Michel Marcus, Sep 19 2018

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A006881, A015910, A162730, A179976.

f[n_]:=With[{f=FactorInteger[n][[All,1]]},PowerMod[ 2,Times@@f,Times@@f] == 2^f[[1]]]; Select[Range[250],PrimeOmega[#]==2&&SquareFreeQ[#]&&f[#]&] (* Harvey P. Dale, Jun 06 2017 *)

isok(n) = {if ((bigomega(n) == 2) && (omega(n) == 2), my(p = factor(n)[1, 1]); lift(Mod(2, n)^n) == 2^p);} \\ Michel Marcus, Sep 19 2018

Definition and terms corrected by R. J. Mathar, Jan 14 2011

A355858 a(n) = n^(2n-1) mod (2n-1).

Original entry on oeis.org

0, 2, 3, 4, 8, 6, 7, 2, 9, 10, 8, 12, 18, 26, 15, 16, 29, 2, 19, 5, 21, 22, 8, 24, 18, 32, 27, 32, 50, 30, 31, 8, 63, 34, 26, 36, 37, 32, 30, 40, 80, 42, 8, 11, 45, 32, 35, 22, 49, 35, 51, 52, 8, 54, 55, 14, 57, 87, 8, 2, 94, 77, 68, 64, 113, 66, 53, 107, 69

Offset: 1

Jonas Kaiser, Jul 20 2022

nonn

If a(n) = n then 2*n-1 is prime or Fermat pseudoprime to base 2.

Cf. A000040, A001567, A006254, A085524, A174166, A179976.

a[n_] := PowerMod[n, 2*n - 1, 2*n - 1]; Array[a, 100] (* Amiram Eldar, Jul 23 2022 *)

PARI
```
a(n)=n^(2*n-1)%(2*n-1)
```

a(n)=lift(Mod(n, 2*n-1)^(2*n-1)) \\ Rémy Sigrist, Jul 21 2022

def a(n): return pow(n, 2*n-1, 2*n-1)
print([a(n) for n in range(1, 70)]) # Michael S. Branicky, Jul 23 2022

cp's OEIS Frontend

A180060 a(n) = 2^(2^n mod n) mod n.

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A180061 Numbers k such that (2^(2^k mod k) mod k) = 4.

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A180074 Squarefree semiprimes s=p*q, p

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A355858 a(n) = n^(2*n-1) mod (2*n-1).

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A355858 a(n) = n^(2n-1) mod (2n-1).