A105825 -id:A105825 - 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

A105824 a(n) = sigma(n) mod 4.

Original entry on oeis.org

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

Offset: 1

Shyam Sunder Gupta, May 05 2005

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

Cf. A000203, A010873, A248150, A072461, A072462, A191217.

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).

A105824:= n-> (numtheory[sigma](n) mod 4):
seq (A105824(n), n=1..105); # Jani Melik, Jan 26 2011

Table[Mod[DivisorSigma[1, n], 4], {n, 100}] (* Wesley Ivan Hurt, Nov 07 2017 *)

PARI
```
a(n)=sigma(n)%4
```

a(n) = A010873(A000203(n)). - Antti Karttunen, Nov 07 2017

A105827 a(n) = sigma(n) (mod 8).

Original entry on oeis.org

1, 3, 4, 7, 6, 4, 0, 7, 5, 2, 4, 4, 6, 0, 0, 7, 2, 7, 4, 2, 0, 4, 0, 4, 7, 2, 0, 0, 6, 0, 0, 7, 0, 6, 0, 3, 6, 4, 0, 2, 2, 0, 4, 4, 6, 0, 0, 4, 1, 5, 0, 2, 6, 0, 0, 0, 0, 2, 4, 0, 6, 0, 0, 7, 4, 0, 4, 6, 0, 0, 0, 3, 2, 2, 4, 4, 0, 0, 0, 2, 1, 6, 4, 0, 4, 4, 0, 4, 2, 2, 0, 0, 0, 0, 0, 4, 2, 3, 4, 1, 6, 0, 0, 2, 0

Offset: 1

Shyam Sunder Gupta, May 05 2005

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

Cf. A000203.

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), A105852 (k=9), A105853 (k=10).

A105827:= (n-> numtheory[sigma](n) mod 8):
seq (A105827(n), n=1..105); # Jani Melik, Jan 26 2011

PARI
```
a(n)=sigma(n)%8
```

A105826 a(n) = sigma(n) (mod 7).

Original entry on oeis.org

1, 3, 4, 0, 6, 5, 1, 1, 6, 4, 5, 0, 0, 3, 3, 3, 4, 4, 6, 0, 4, 1, 3, 4, 3, 0, 5, 0, 2, 2, 4, 0, 6, 5, 6, 0, 3, 4, 0, 6, 0, 5, 2, 0, 1, 2, 6, 5, 1, 2, 2, 0, 5, 1, 2, 1, 3, 6, 4, 0, 6, 5, 6, 1, 0, 4, 5, 0, 5, 4, 2, 6, 4, 2, 5, 0, 5, 0, 3, 4, 2, 0, 0, 0, 3, 6, 1, 5, 6, 3, 0, 0, 2, 4, 1, 0, 0, 3, 2, 0, 4, 6, 6, 0, 3

Offset: 1

Shyam Sunder Gupta, May 05 2005

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

Cf. A000203.

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).

A105826:= n-> (numtheory[sigma](n) mod 7):
seq (A105826(n), n=1..105); # Jani Melik, Jan 26 2011

Mod[DivisorSigma[1,Range[110]],7] (* Harvey P. Dale, Jul 30 2021 *)

PARI
```
a(n)=sigma(n)%7
```

A105853 a(n) = sigma(n) (mod 10), i.e., unit's digit of sigma(n).

Original entry on oeis.org

1, 3, 4, 7, 6, 2, 8, 5, 3, 8, 2, 8, 4, 4, 4, 1, 8, 9, 0, 2, 2, 6, 4, 0, 1, 2, 0, 6, 0, 2, 2, 3, 8, 4, 8, 1, 8, 0, 6, 0, 2, 6, 4, 4, 8, 2, 8, 4, 7, 3, 2, 8, 4, 0, 2, 0, 0, 0, 0, 8, 2, 6, 4, 7, 4, 4, 8, 6, 6, 4, 2, 5, 4, 4, 4, 0, 6, 8, 0, 6, 1, 6, 4, 4, 8, 2, 0, 0, 0, 4, 2, 8, 8, 4, 0, 2, 8, 1, 6, 7, 2, 6, 4, 0, 2

Offset: 1

Shyam Sunder Gupta, May 05 2005

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A000203, A010879.

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), A105852 (k=9), A105853 (k=10).

A105853:=n->(numtheory)[sigma](n) mod 10: seq(A105853(n), n=1..180); # Wesley Ivan Hurt, Nov 07 2017

Mod[DivisorSigma[1,Range[110]],10] (* Harvey P. Dale, May 20 2019 *)

PARI
```
a(n)=sigma(n)%10
```

a(n) = A010879(A000203(n)). - Michel Marcus, Jul 26 2017

cp's OEIS Frontend

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

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A105824 a(n) = sigma(n) mod 4.

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A105827 a(n) = sigma(n) (mod 8).

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A105826 a(n) = sigma(n) (mod 7).

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A105853 a(n) = sigma(n) (mod 10), i.e., unit's digit of sigma(n).

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Programs

Maple

Mathematica

PARI

Formula