A054022 -id:A054022 - cp's OEIS frontend

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

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 *)

A160550 a(n) = A001065(n) mod A000005(n).

Original entry on oeis.org

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

Offset: 1

Ctibor O. Zizka, May 19 2009

A054022(n) for n > 1 gives the numbers k such that a(k) = 1.

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

Cf. A000203, A000027, A000005, A054022, A001065, A003601, A140480.

[ (SumOfDivisors(n)-n) mod NumberOfDivisors(n): n in [1..105] ]; // Klaus Brockhaus, May 21 2009

Table[Mod[DivisorSigma[1,n]-n,DivisorSigma[0,n]],{n,110}] (* Harvey P. Dale, Jun 22 2013 *)

A160550(n)=lift(Mod(sigma(n)-n,numdiv(n))); \\ Michael B. Porter, Oct 13 2009

Extended and comment edited by Klaus Brockhaus, May 21 2009

cp's OEIS Frontend

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

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