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 A129487 Unitary deficient numbers. 12
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 7 15:01 EST 2022. Contains 358667 sequences. (Running on oeis4.)