login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A127653 Integers whose unitary aliquot sequences terminate in 0, including 1 but excluding the other trivial cases in which n is itself either a prime or a prime power. 5
1, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 33, 34, 35, 36, 38, 39, 40, 44, 45, 46, 48, 50, 51, 52, 55, 56, 57, 58, 62, 63, 65, 68, 69, 70, 72, 74, 75, 76, 77, 80, 82, 84, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 98, 99 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

Riele, H. J. J. te; Unitary Aliquot Sequences. MR 139/72, Mathematisch Centrum, 1972, Amsterdam.

Riele, H. J. J. te; Further Results On Unitary Aliquot Sequences. NW 2/73, Mathematisch Centrum, 1973, Amsterdam.

LINKS

Table of n, a(n) for n=1..56.

EXAMPLE

a(5)=15 because the fifth integer that is neither prime nor a prime power and whose unitary aliquot sequence terminates in 0 is 15.

MATHEMATICA

UnitaryDivisors[n_Integer?Positive] := Select[Divisors[n], GCD[ #, n/# ] == 1 \ &]; sstar[n_] := Plus @@ UnitaryDivisors[ n] - n; pp[k_] := If[Length[ FactorInteger[k]] == 1, True, False]; g[n_] := If[n > 0, sstar[n], 0]; UnitaryTrajectory[n_] := Most[NestWhileList[g, n, UnsameQ, All]]; Select[Range[100], Last[UnitaryTrajectory[ # ]] == 0 && ! pp[ # ] &]

CROSSREFS

Cf. A127652, A097032, A097010, A098185, A127654, A063991, A097037, A097036.

Sequence in context: A206286 A116023 A062408 * A050705 A095406 A337028

Adjacent sequences: A127650 A127651 A127652 * A127654 A127655 A127656

KEYWORD

hard,nonn

AUTHOR

Ant King, Jan 24 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 16:00 EST 2022. Contains 358644 sequences. (Running on oeis4.)