

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
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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



