A084300 -id:A084300 - cp's OEIS frontend

A084301 a(n) = sigma(n) mod 6.

1, 3, 4, 1, 0, 0, 2, 3, 1, 0, 0, 4, 2, 0, 0, 1, 0, 3, 2, 0, 2, 0, 0, 0, 1, 0, 4, 2, 0, 0, 2, 3, 0, 0, 0, 1, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 4, 3, 3, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 1, 0, 0, 2, 0, 0, 0, 0, 3, 2, 0, 4, 2, 0, 0, 2, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 3, 0, 1, 0, 0, 2, 0, 0

Offset: 1

Labos Elemer, Jun 02 2003

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to sums of divisors

Cf. A000203, A010875, A054763, A084299, A084300.
Sequences sigma(n) mod k: A053866 (k=2), A074941 (k=3), A105824 (k=4), A105825 (k=5), A084301 (k=6), A105826 (k=7), A105827 (k=8).
Cf. A074627 (locations of 0), A074628 (locations of 2), A067051 (locations of 3), A074630 (locations of 4), A074384 (locations of 5).

A084301:= n-> (numtheory[sigma](n) mod 6):
seq (A084301(n), n=1..105); # Jani Melik, Jan 26 2011

Table[Mod[DivisorSigma[1,n],6],{n,120}]  (* Harvey P. Dale, Apr 07 2011 *)

a(n)=sigma(n)%6 \\ Charles R Greathouse IV, Mar 09 2014

a(n) = A010875(A000203(n)). - Antti Karttunen, Nov 07 2017

A074942 a(n) = phi(n) mod 3.

Original entry on oeis.org

1, 1, 2, 2, 1, 2, 0, 1, 0, 1, 1, 1, 0, 0, 2, 2, 1, 0, 0, 2, 0, 1, 1, 2, 2, 0, 0, 0, 1, 2, 0, 1, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 1, 1, 1, 0, 2, 2, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 1, 0, 1, 0, 2, 1, 1, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 1, 1, 2, 0, 0, 0

Offset: 1

Benoit Cloitre, Oct 04 2002

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000010, A010872, A074943, A084300.

[EulerPhi(n) mod 3: n in [1..110]]; // Vincenzo Librandi, Sep 04 2015

Table[Mod[EulerPhi[n], 3], {n, 100}] (* Vincenzo Librandi, Sep 04 2015 *)

PARI
```
a(n)=eulerphi(n)%3
```

a(n) = A000010(n) mod 3.

a(n) = A010872(A000010(n)). - Michel Marcus, Sep 05 2015

A353768 a(n) = phi(n) mod 4; Euler totient function reduced modulo 4.

Original entry on oeis.org

1, 1, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2

Offset: 1

Antti Karttunen, May 15 2022

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000010, A010873, A066499 (positions of 2's), A172019 (of 0's).

Cf. also A074942, A261872, A084300, and also A105824.

PARI
```
A353768(n) = (eulerphi(n)%4);
```

a(n) = A010873(A000010(n)).

A261872 a(n) = phi(n) mod 5, where phi is the Euler totient function.

Original entry on oeis.org

1, 1, 2, 2, 4, 2, 1, 4, 1, 4, 0, 4, 2, 1, 3, 3, 1, 1, 3, 3, 2, 0, 2, 3, 0, 2, 3, 2, 3, 3, 0, 1, 0, 1, 4, 2, 1, 3, 4, 1, 0, 2, 2, 0, 4, 2, 1, 1, 2, 0, 2, 4, 2, 3, 0, 4, 1, 3, 3, 1, 0, 0, 1, 2, 3, 0, 1, 2, 4, 4, 0, 4, 2, 1, 0, 1, 0, 4, 3, 2, 4, 0, 2, 4, 4, 2, 1, 0, 3, 4, 2, 4, 0, 1, 2, 2, 1, 2, 0, 0, 0, 2, 2, 3, 3

Offset: 1

Vincenzo Librandi, Sep 04 2015

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A000010, A010874, A074942, A084300.

Magma
```
[EulerPhi(n) mod 5: n in [1..110]];
```
Mathematica
```
Table[Mod[EulerPhi[n], 5], {n, 110}]
```

a(n) = eulerphi(n) % 5; \\ Michel Marcus, Sep 05 2015

a(n) = A000010(n) mod 5 = A010874(A000010(n)).

More terms from Antti Karttunen, Dec 04 2017

A084302 Remainder of tau(n) modulo 6.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 0, 2, 4, 4, 5, 2, 0, 2, 0, 4, 4, 2, 2, 3, 4, 4, 0, 2, 2, 2, 0, 4, 4, 4, 3, 2, 4, 4, 2, 2, 2, 2, 0, 0, 4, 2, 4, 3, 0, 4, 0, 2, 2, 4, 2, 4, 4, 2, 0, 2, 4, 0, 1, 4, 2, 2, 0, 4, 2, 2, 0, 2, 4, 0, 0, 4, 2, 2, 4, 5, 4, 2, 0, 4, 4, 4, 2, 2, 0, 4, 0, 4, 4, 4, 0, 2, 0, 0, 3, 2, 2, 2, 2, 2

Offset: 1

Labos Elemer, Jun 02 2003

The sums of the first 10^k terms, for k = 1, 2, ..., are 27, 236, 2275, 22166, 220070, 2195376, 21933228, 219259514, 2192385128, 21923168052, ... . Conjecture: the asymptotic mean of this sequence is 3*zeta(3)/zeta(2) = 3 * A253905 = 2.192288... . The conjecture is true if A211337 and A211338 have an equal asymptotic density (see also A059269). - Amiram Eldar, Jul 11 2024

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences computed from exponents in factorization of n.

Cf. A000005, A054763, A084299, A084300, A084301.

Cf. A059269, A211337, A211338

Mod[DivisorSigma[0,Range[110]],6] (* Harvey P. Dale, Sep 04 2020 *)

A084302(n) = (numdiv(n)%6); \\ Antti Karttunen, Jul 07 2017

a(n) = A000005(n) modulo 6.

cp's OEIS Frontend

A084301 a(n) = sigma(n) mod 6.

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A074942 a(n) = phi(n) mod 3.

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A353768 a(n) = phi(n) mod 4; Euler totient function reduced modulo 4.

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A261872 a(n) = phi(n) mod 5, where phi is the Euler totient function.

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Magma

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A084302 Remainder of tau(n) modulo 6.

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