|
| |
|
|
A005278
|
|
Noncototients: n such that x - phi(x) = n has no solution.
(Formerly M4688)
|
|
20
|
|
|
|
10, 26, 34, 50, 52, 58, 86, 100, 116, 122, 130, 134, 146, 154, 170, 172, 186, 202, 206, 218, 222, 232, 244, 260, 266, 268, 274, 290, 292, 298, 310, 326, 340, 344, 346, 362, 366, 372, 386, 394, 404, 412, 436, 466, 470, 474, 482, 490, 518, 520
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
If the strong Goldbach conjecture (every even number>6 is the sum of at least 2 distinct primes p and q) is true, sequence contains only even values. Since p*q-phi(p*q)=p+q-1 and then every odd number can be expressed as x-phi(x). - Benoit Cloitre, Mar 03 2002
|
|
|
REFERENCES
|
J. Browkin and A. Schinzel, On integers not of the form n-phi(n), Colloq. Math., 68 (1995), 55-58. [Shows that this sequence is infinite. - Labos E. (labos(AT)ana.sote.hu), Dec 21 1999]
R. K. Guy, Unsolved Problems in Number Theory, B36.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
|
T. D. Noe and Donovan Johnson, Table of n, a(n) for n = 1..10000 (first 963 terms from T. D. Noe)
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
Eric Weisstein's World of Mathematics, Noncototient
|
|
|
MATHEMATICA
|
nmax = 520; cototientQ[n_?EvenQ] := (x = n; While[test = x - EulerPhi[x] == n ; Not[test || x > 2*nmax], x++]; test); cototientQ[n_?OddQ] = True; Select[Range[nmax], !cototientQ[#]&] (* Jean-François Alcover, Jul 20 2011 *)
|
|
|
CROSSREFS
|
Cf. A006093, A126887. Complement of A051953.
Sequence in context: A043342 A023715 A045143 * A157075 A045039 A080059
Adjacent sequences: A005275 A005276 A005277 * A005279 A005280 A005281
|
|
|
KEYWORD
|
nonn,nice
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
EXTENSIONS
|
More terms from Jud McCranie 1/97.
|
|
|
STATUS
|
approved
|
| |
|
|
