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A005114 Untouchable numbers: impossible values for sum of aliquot parts of n.
(Formerly M1552)
31
2, 5, 52, 88, 96, 120, 124, 146, 162, 188, 206, 210, 216, 238, 246, 248, 262, 268, 276, 288, 290, 292, 304, 306, 322, 324, 326, 336, 342, 372, 406, 408, 426, 430, 448, 472, 474, 498, 516, 518, 520, 530, 540, 552, 556, 562, 576, 584, 612, 624, 626, 628, 658 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Chen & Zhao show that the lower density of this sequence is at least 0.06, improving on te Riele. - Charles R Greathouse IV, Dec 28 2013

REFERENCES

Jack David Alanen, Empirical study of aliquot series. Ph.D Thesis, Yale University, 1972.

Yong-Gao Chen and Qing-Qing Zhao, Nonaliquot numbers, Publ. Math. Debrecen 78:2 (2011), pp. 439-442.

R. K. Guy, Unsolved Problems in Number Theory, B10.

Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 65.

H. J. J. te Riele, A Theoretical and Computational Study of Generalized Aliquot Sequences (Dissertation). Mathematisch Centrum, Amsterdam, 1975.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Klaus Brockhaus, Table of n, a(n) for n = 1..8153

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy], p. 840.

P. Erdős, Ueber die Zahlen der Form sigma(n)-n und n-phi(n), Elemente der Math. 28 (1973), pp. 83-86.

C. Pomerance and H.-S. Yang, On untouchable numbers and related problems, 2012.

C. Pomerance and H.-S. Yang, Variant of a theorem of Erdos on the sum-of-proper-divisors function, 2012.

Giovanni Resta, Untouchable numbers the 150232 terms up to 10^6

Eric Weisstein's World of Mathematics, Untouchable Number.

Wikipedia, Untouchable number

FORMULA

Complement of A078923. - Lekraj Beedassy, Jul 19 2005

MATHEMATICA

untouchableQ[n_] := Catch[ Do[ If[n == DivisorSigma[1, k]-k, Throw[True]], {k, 0, (n-1)^2}]] === Null; Reap[ Table[ If[ untouchableQ[n], Print[n]; Sow[n]], {n, 2, 700}]][[2, 1]] (* Jean-François Alcover, Jun 29 2012, after Benoit Cloitre *)

PROG

(PARI) isA078923(n)=if(n==0 || n==1, return(1)); for(m=1, (n-1)^2, if( sigma(m)-m == n, return(1))); 0

isA005114(n)=!isA078923(n)

for(n=1, 700, if (isA005114(n), print(n))) \\ R. J. Mathar, Aug 10 2006

CROSSREFS

Cf. A064000.

Sequence in context: A208797 A004098 A208206 * A216079 A206584 A081090

Adjacent sequences:  A005111 A005112 A005113 * A005115 A005116 A005117

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from David W. Wilson

STATUS

approved

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Last modified April 24 05:09 EDT 2014. Contains 240953 sequences.