A230605 -id:A230605 - cp's OEIS frontend

A140826 Arithmetic nondivisor means.

3, 4, 5, 7, 11, 13, 17, 18, 19, 20, 23, 24, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269

Offset: 1

Ctibor O. Zizka, Jul 17 2008

Numbers n such that A024816(n)/(n-A000005(n)) is an integer.
Numbers n such that A231167(n) = 0. - Jaroslav Krizek, Nov 07 2013
Union of odd primes (A065091) and composites from A230605 (4, 18, 20, 24, 432, 588...). - Jaroslav Krizek, Nov 07 2013

			n=18: numbers less than n which do not divide n are 4,5,7,8,10,11,12,13,14,15,16,17.
antisigma_1(18) = 4+5+7+8+10+11+12+13+14+15+16+17 = 132.
antisigma_0(18) = 12.
132/12 = 11 which is an integer so n=18 belongs to the sequence.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000005, A003601, A024816, A049820, A000203.

A024816 := proc(n) n*(n+1)/2-numtheory[sigma](n) ; end:
isA140826 := proc(n) if A024816(n) mod ( n-A000005(n)) = 0 then true; else false; fi; end:
for n from 3 to 400 do if isA140826(n) then printf("%d,",n) ; fi; od: # R. J. Mathar, Dec 13 2008

Select[Range[3, 300], IntegerQ[(#^2 + # - 2 DivisorSigma[1, #])/(2# - 2 DivisorSigma[0, #])]&] (* Jean-François Alcover, May 11 2023 *)

isok(n) = (nnd = n - numdiv(n)) && !((n*(n+1)/2-sigma(n)) % nnd); \\ Michel Marcus, Nov 09 2013

Numbers n such that (n*n+n-2*A000203(n))/(2*n-2*A000005(n)) is an integer.

Inserted 20 and extended by R. J. Mathar, Dec 13 2008

A231167 a(1) = a(2) = 0, for n>=3: (sum of non-divisors of n) modulo (number of non-divisors of n).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 0, 2, 0, 1, 8, 6, 0, 0, 0, 0, 12, 1, 0, 0, 8, 1, 16, 20, 0, 19, 0, 23, 20, 1, 24, 8, 0, 1, 24, 26, 0, 25, 0, 32, 21, 1, 0, 26, 18, 38, 32, 38, 0, 31, 40, 36, 36, 1, 0, 30, 0, 1, 31, 15, 48, 37, 0, 50, 44, 47, 0, 33, 0, 1, 35, 56

Offset: 1

Jaroslav Krizek, Nov 07 2013

nonn

a(n) = 0 for n = 1, 2 and numbers from A140826.

a(n) = 1 for numbers of form 2*p (p=prime) from A100484 and other numbers, e.g. 8 and 13456 are only numbers n < 10^5 which are not of form 2*p with a(n) = 1.

			For n=6, a(6) = A024816(6) mod A049820(6) = 9 mod 2 = 1.

Jaroslav Krizek, Table of n, a(n) for n = 1..10000

Cf. A054025 (sigma(n) mod tau(n)), A024816, A049820, A024816, A049820, A065091, A230605, A161344.

ndn[n_]:=Module[{nd=Complement[Range[n],Divisors[n]]},Mod[Total[ nd],Length[ nd]]]; Join[{0,0},Array[ndn,80,3]] (* Harvey P. Dale, Apr 11 2022 *)

a(n) = A024816(n) mod A049820(n).

cp's OEIS Frontend

A140826 Arithmetic nondivisor means.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

Extensions