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A083243 Numbers n for which there are more divisors and coprimes than other numbers less than n: A045763(n) < A073757(n) or A045763(n)<n/2 or A073757(n)>n/2. 9
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Complement of A083244 = (42, 54, 60, 66, 70, 72, 78, ...). - M. F. Hasler, Jan 18 2015

LINKS

Table of n, a(n) for n=1..72.

FORMULA

d(n) + phi(n) - 1 < n/2

EXAMPLE

n=146 is here because it has d=4 divisors, r=72 numbers are coprimes and u=71 are unrelated: d+r-1=4+72-1=75>n/2=146/2=73>71=u.

n=61455 is here because has 16 divisors and equal number of coprimes and unrelated numbers u=r=30720: d+r-1-30735>30720.

MATHEMATICA

Do[r=EulerPhi[n]; d=DivisorSigma[0, n]; u=n-r-d+1; If[Greater[n-u, n/2], Print[n, {d, r, u}]], {n, 1, 100}]

CROSSREFS

Cf. A000005, A000010, A045763, A073757, A020488, A083244, A083245.

Sequence in context: A044923 A180925 A247151 * A002837 A056561 A236674

Adjacent sequences:  A083240 A083241 A083242 * A083244 A083245 A083246

KEYWORD

nonn

AUTHOR

Labos Elemer, May 07 2003

STATUS

approved

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Last modified August 29 03:31 EDT 2015. Contains 261184 sequences.