A222313 A222311 sorted and duplicates removed (conjectured).

1, 2, 3, 5, 6, 15, 17, 33, 41, 55, 57, 65, 70, 105, 129, 257, 273, 385, 561, 897, 969, 1001, 1105, 1353, 1430, 1785, 2049, 2145, 2337, 2665, 3553, 4097, 4305, 4745, 4845, 5633, 6105, 6545, 8193, 8385

Offset: 1

Author

N. J. A. Sloane, Feb 16 2013

Keywords

• nonn
• more

Comments

Obtained by sorting and removing duplicates from the first 500 terms of A222311. There is no proof as yet that this list is complete up to 105. Only the first three terms shown are certain. Is there a proof that 4 cannot appear?

Links

• Cristian Cobeli, Mihai Prunescu, Alexandru Zaharescu, A growth model based on the arithmetic Z-game, arXiv:1511.04315 [math.NT], 2015.
• Cristian Cobeli, Alexandru Zaharescu, A game with divisors and absolute differences of exponents, arXiv:1411.1334 [math.NT], 2014 (see page 12).

Crossrefs

Cf. A222310, A222311.

Programs

Mathematica

terms = 40; nmax0 = 5000;
seq[nmax_] := seq[nmax] = Union[Print[nmax]; Join[r = {1}, Table[Reverse[r = FoldList[#1*(#2/GCD[#1, #2]^2) & , n, r]], {n, 2, nmax}][[All, 1]]]][[1 ;; terms]];
seq[nmax = nmax0]; seq[nmax = 2 nmax]; While[seq[nmax] == seq[nmax/2], nmax = 2 nmax]; seq[nmax] (* Jean-François Alcover, Sep 04 2018, after Ivan Neretin in A222310 *)

Extensions

Corrected and extended using data from Cobeli et al., 2015. - N. J. A. Sloane, Aug 27 2016

More terms (computed from a list of 10000) from Jean-François Alcover, Sep 04 2018