

A064000


Unitary untouchable numbers of second kind: numbers n such that usigma(x) = n has no solution, where usigma(x) (A034448) is the sum of unitary divisors of x.


6



2, 7, 11, 13, 15, 16, 19, 21, 22, 23, 25, 27, 29, 31, 34, 35, 37, 39, 41, 43, 45, 46, 47, 49, 51, 52, 53, 55, 57, 58, 59, 61, 63, 64, 66, 67, 69, 71, 73, 75, 76, 77, 79, 81, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 99, 101, 103, 105, 106, 107, 109, 111, 113, 115, 116
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OFFSET

1,1


LINKS

Donovan Johnson, Table of n, a(n) for n = 1..10000
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 sumofproperdivisors function, 2012


FORMULA

Suppose usigma(x)=n. Then by definition usigma(x)=n>1 for n>1. Let x be a prime. Then usigma(x)=x+1 and so n=x+1. For x not prime, of course, x+1<n. So in general x<=n1.


MATHEMATICA

usigma[n_] := Sum[ Boole[GCD[d, n/d] == 1]*d, {d, Divisors[n]}]; untouchableQ[n_] := (r = True; x = 1; While[x <= n, If[usigma[x] == n, r = False; Break[], x++]]; r); Select[Range[120], untouchableQ] (* JeanFrançois Alcover, Jan 03 2013 *)


CROSSREFS

Cf. A034448, A063948.
Sequence in context: A230048 A201362 A063976 * A069180 A253898 A173135
Adjacent sequences: A063997 A063998 A063999 * A064001 A064002 A064003


KEYWORD

easy,nonn


AUTHOR

Labos Elemer and Felice Russo, Sep 05 2001


EXTENSIONS

Edited by N. J. A. Sloane, May 04 2007


STATUS

approved



