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A140826 Arithmetic nondivisor means. 5
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..60.

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

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: A047499 A082378 A046642 * A081735 A227231 A107036

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

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Last modified March 20 23:22 EDT 2019. Contains 321354 sequences. (Running on oeis4.)