A248857 Composite numbers n such that n - phi(n) is a power of 10.

1320, 1640, 1768, 1996, 13200, 16400, 19984, 19996, 132000, 164000, 199996, 1320000, 1640000, 1999936, 13200000, 16400000, 16666240, 17999488, 18515584, 19999984, 19999996, 132000000, 164000000, 164296960, 166662400, 199999936, 199999984, 1320000000

Offset

1,1

Comments

Numbers n such that n - phi(n) is a positive power of 10.

Numbers n such that phi(n) = n - 10^floor(log(10,n)).

The most significant digit of all terms is equal to 1, since all terms are even and for even numbers n, phi(n) <= n/2.

If p = 5^(2n-1)*10^m-1 is prime then s = 4^n*p is in the sequence, because s - phi(s) = 10^(2n+m-1).

For n=1,2, ..., 6, ... smallest such term of the sequence respectively are 1996, 19984, 1999936, 1999999744, 19999999998976,19999999995904, ... .

Sequence A248858 gives number of digits of these terms.

Links

Giovanni Resta, Table of n, a(n) for n = 1..47 (terms < 10^12, first 41 terms from Robert G. Wilson v)

Example

1320 is in the sequence because 1320 - phi(1320) = 10^3.

Mathematica

a248857[n_] := Select[Select[Range@n, CompositeQ[#] &], IntegerQ[Log10[# - EulerPhi[#]]] &]; a248857[10^7] (* Michael De Vlieger, Jan 07 2015 *)

Prog

(PARI) lista(nn) = forcomposite(n=2, nn, if (ispower(n-eulerphi(n), , &d) && (d==10), print1(n, ", "))); \\ Michel Marcus, Jan 06 2015

Crossrefs

Cf. A000010, A067206, A066663, A244440, A248854, A248858.

Sequence in context: A023318 A066663 A067206 * A260839 A157266 A069737

Adjacent sequences: A248854 A248855 A248856 * A248858 A248859 A248860

Keyword

nonn

Author

Farideh Firoozbakht, Dec 31 2014

Extensions

a(22)-a(28) from Giovanni Resta, Apr 17 2017

Status

approved