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

1,1

Comments

Numbers n such that a(n)=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

Links

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

Formula

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

Example

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
sigma_0(18) = 12
132/12 = 11 which is an integer so n=18 belongs to the sequence.

Maple

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A330110 A330123 A354711 * A081735 A373142 A227231

Adjacent sequences: A140823 A140824 A140825 * A140827 A140828 A140829

Keyword

easy,nonn

Author

Ctibor O. Zizka, Jul 17 2008

Extensions

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

Status

approved