A129487 Unitary deficient numbers.

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

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 A351227 A132999

Adjacent sequences: A129484 A129485 A129486 * A129488 A129489 A129490

Keyword

easy,nonn

Author

Ant King, Apr 20 2007

Status

approved