

A129487


Unitary deficient numbers.


9



1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 79
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OFFSET

1,2


COMMENTS

The unitary deficient numbers account for almost 93% of all integers (including all primes (A000040) and prime powers (A000961)) and asymptotically satisfy a(n)~1.0753n. This provides an excellent fit as n grows larger. For example, the one millionth unitary deficient number is 1075293 and the asserted approximation returns 1075300, giving an error of only 0.00065%.


LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..10000


FORMULA

Integers for which A034460(n) < n, or equivalently for which A034448(n) < 2n.


EXAMPLE

The sixth integer that exceeds the sum of its proper unitary divisors is 7. Hence a(6)=7.


MAPLE

a := proc(n) numtheory[divisors](n); select(d > igcd(d, n/d)=1, %); `if`(add(i, i=%) < 2*n, n, NULL) end: # Peter Luschny, May 03 2009


MATHEMATICA

UnitaryDivisors[n_Integer?Positive]:=Select[Divisors[n], GCD[ #, n/# ]==1&]; Select[Range[100], Plus@@UnitaryDivisors[ # ]2#<0 &]


CROSSREFS

Cf. A034460, A034448, A129468, A034683, A000040, A000961.
Sequence in context: A161924 A034153 A004725 * A097010 A132999 A054027
Adjacent sequences: A129484 A129485 A129486 * A129488 A129489 A129490


KEYWORD

easy,nonn


AUTHOR

Ant King, Apr 20 2007


STATUS

approved



