A054014 -id:A054014 - 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

A054015 a(n) is Chowla function of n read modulo (number of proper divisors of n), a(1) = 0 by convention.

Original entry on oeis.org

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

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
Index entries for sequences related to sums of divisors

Cf. A032741, A048050, A054013, A054014.

with(numtheory): [seq((sigma(i)-i-1) mod (tau(i)-1),i=2..120);#i>1

A054015(n) = if(1==n,0,((sigma(n)-n-1) % (numdiv(n)-1))); \\ Antti Karttunen, Oct 20 2017

a(1) = 0; for n > 1, a(n) = A048050(n) mod A032741(n).

Description clarified by Antti Karttunen, Oct 20 2017

A054022 Chowla function of n is divisible by the number of divisors of n.

Original entry on oeis.org

1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 23, 27, 29, 31, 32, 35, 36, 37, 39, 41, 43, 47, 50, 51, 53, 55, 59, 61, 67, 71, 73, 75, 79, 83, 87, 89, 91, 95, 97, 98, 101, 103, 107, 109, 111, 113, 115, 119, 123, 127, 131, 135, 137, 139, 143, 149, 151, 155, 157, 159, 162, 163

Offset: 1

Asher Auel, Jan 19 2000

nonn

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

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

Complement is A054023 Cf. A000005, A048050, A054014.

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

Select[Range[200],Divisible[DivisorSigma[1,#]-1-#,DivisorSigma[0,#]]&] (* Harvey P. Dale, Mar 11 2012 *)

A054023 Chowla function of n is not divisible by the number of divisors of n.

Original entry on oeis.org

4, 6, 8, 10, 12, 14, 16, 18, 20, 21, 22, 24, 25, 26, 28, 30, 33, 34, 38, 40, 42, 44, 45, 46, 48, 49, 52, 54, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 76, 77, 78, 80, 81, 82, 84, 85, 86, 88, 90, 92, 93, 94, 96, 99, 100, 102, 104, 105, 106, 108, 110, 112, 114

Offset: 1

Asher Auel, Jan 19 2000

nonn

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Complement is A054022.

Cf. A000005, A048050, A054014.

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

cfQ[n_]:=!Divisible[DivisorSigma[1,n]-1-n,DivisorSigma[0,n]]; Select[ Range[ 150],cfQ] (* Harvey P. Dale, Jul 22 2014 *)

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A054013 Chowla function of n read modulo n.

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A054015 a(n) is Chowla function of n read modulo (number of proper divisors of n), a(1) = 0 by convention.

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A054022 Chowla function of n is divisible by the number of divisors of n.

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Mathematica

A054023 Chowla function of n is not divisible by the number of divisors of n.

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Author

Keywords

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Links

Crossrefs

Programs

Maple

Mathematica