A054015 -id:A054015 - cp's OEIS frontend

A054013 Chowla function of n read modulo n.

0, 0, 0, 2, 0, 5, 0, 6, 3, 7, 0, 3, 0, 9, 8, 14, 0, 2, 0, 1, 10, 13, 0, 11, 5, 15, 12, 27, 0, 11, 0, 30, 14, 19, 12, 18, 0, 21, 16, 9, 0, 11, 0, 39, 32, 25, 0, 27, 7, 42, 20, 45, 0, 11, 16, 7, 22, 31, 0, 47, 0, 33, 40, 62, 18, 11, 0, 57, 26, 3, 0, 50, 0, 39, 48, 63, 18, 11, 0, 25, 39, 43, 0

Offset: 1

Asher Auel, Jan 17 2000

nonn

Chowla's function (A048050) = sum of divisors of n except 1 and n.

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

Cf. A048050, A054014, A054015.

with(numtheory): [seq((sigma(i) - i - 1) mod i, i=2..100)];

Table[Mod[DivisorSigma[1,n]-n-1,n],{n,90}] (* Harvey P. Dale, Dec 01 2011 *)

A054013(n) = ((sigma(n)-n-1) % n); \\ Antti Karttunen, Oct 30 2017

a(n) = A048050(n) mod n

A054014 Chowla function of n read modulo (the number of divisors of n).

Original entry on oeis.org

0, 0, 0, 2, 0, 1, 0, 2, 0, 3, 0, 3, 0, 1, 0, 4, 0, 2, 0, 3, 2, 1, 0, 3, 2, 3, 0, 3, 0, 1, 0, 0, 2, 3, 0, 0, 0, 1, 0, 1, 0, 5, 0, 3, 2, 1, 0, 5, 1, 0, 0, 3, 0, 1, 0, 7, 2, 3, 0, 11, 0, 1, 4, 6, 2, 5, 0, 3, 2, 1, 0, 2, 0, 3, 0, 3, 2, 1, 0, 5, 4, 3, 0, 7, 2, 1, 0, 3, 0, 11, 0, 3, 2, 1, 0, 11, 0, 0, 2, 8, 0, 1, 0

Offset: 1

Asher Auel, Jan 17 2000

nonn

Chowla's function (A048050) = sum of divisors of n except 1 and n.

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

Cf. A000005, A048050, A054013, A054015.

with(numtheory): [seq((sigma(i)-i-1) mod tau(i),i=1..120)];

Array[Mod[DivisorSigma[1, #] - # - 1, DivisorSigma[0, #]] &, 103] (* Michael De Vlieger, Oct 30 2017 *)

A054014(n) = ((sigma(n)-n-1) % numdiv(n)); \\ Antti Karttunen, Oct 30 2017

a(n) = A048050(n) mod A000005(n).

A054020 Chowla's function of n is not divisible by the number of proper divisors of n.

Original entry on oeis.org

6, 9, 10, 15, 16, 20, 21, 22, 25, 28, 30, 33, 34, 36, 39, 42, 44, 45, 46, 48, 49, 50, 51, 54, 55, 57, 58, 60, 64, 68, 69, 70, 72, 75, 76, 78, 80, 81, 82, 84, 85, 87, 91, 93, 94, 96, 98, 99, 100, 102, 105, 106, 108, 111, 114, 115, 116, 117, 118, 120, 121, 123, 124, 126

Offset: 1

Asher Auel, Jan 19 2000

nonn

Chowla's function (A048050) = sum of divisors of n except 1 and n.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Complement is A054021.

Cf. A032741, A048050, A054015.

with(numtheory):
[seq(`if`((sigma(i)-i-1) mod (tau(i)-1) <> 0,i,print( )),i=2..500)];

Select[Range[2,150],!Divisible[DivisorSigma[1,#]-#-1,DivisorSigma[ 0,#]- 1]&] (* Harvey P. Dale, May 27 2014 *)

A054021 Numbers n such that Chowla's function of n is divisible by the number of proper divisors of n.

Original entry on oeis.org

2, 3, 4, 5, 7, 8, 11, 12, 13, 14, 17, 18, 19, 23, 24, 26, 27, 29, 31, 32, 35, 37, 38, 40, 41, 43, 47, 52, 53, 56, 59, 61, 62, 63, 65, 66, 67, 71, 73, 74, 77, 79, 83, 86, 88, 89, 90, 92, 95, 97, 101, 103, 104, 107, 109, 110, 112, 113, 119, 122, 125, 127, 128, 131, 134, 136

Offset: 1

Asher Auel, Jan 19 2000

nonn

Chowla's function (A048050) = sum of divisors of n except 1 and n.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Complement is A054020.

Cf. A032741, A048050, A054015.

with(numtheory):
[seq(`if`((sigma(i)-i-1) mod (tau(i)-1)=0,i,print( )),i=2..1000)];

Select[Range[2,150],Divisible[DivisorSigma[1,#]-1-#,DivisorSigma[ 0,#]-1]&] (* Harvey P. Dale, Aug 13 2018 *)

cp's OEIS Frontend

A054013 Chowla function of n read modulo n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A054014 Chowla function of n read modulo (the number of divisors of n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A054020 Chowla's function of n is not divisible by the number of proper divisors of n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

A054021 Numbers n such that Chowla's function of n is divisible by the number of proper divisors of n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica