A070980 Numbers k such that the number of steps to reach 1 in '3x+1' problem equals tau(k), the number of divisors of k.

40, 42, 96, 180, 280, 1664, 1704, 1932, 1960, 2184, 2304, 2310, 4816, 4928, 7252, 9360, 9792, 12888, 12896, 13338, 13720, 14256, 15792, 16240, 17408, 17940, 17952, 18096, 20000, 20016, 21200, 21450, 25080, 25600, 27136, 28980, 30016, 31808, 34048, 34240, 34320, 34368, 35028, 36576, 36652, 37332, 38088, 39936, 45056, 47880

Offset

1,1

Comments

Are all terms even?

Numbers k such that A006577(k) = A000005(k).

Not all terms are even. In the first 200 terms, three are odd: 82485, 91665, and 337365. - Harvey P. Dale, Feb 16 2014

Links

Harvey P. Dale, Table of n, a(n) for n = 1..200

Mathematica

nsQ[n_]:=Length[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #!=1&]]-1 == DivisorSigma[ 0, n]; Select[Range[50000], nsQ] (* Harvey P. Dale, Feb 15 2014 *)

Prog

(PARI) for(n=1, 40000, s=n; t=0; while(s!=1, t++; if(s%2==0, s=s/2, s=3*s+1); if(s==if(numdiv(n)-t, 0, 1), print1(n, ", "); ); ))

Crossrefs

Sequence in context: A128843 A214563 A111167 * A131535 A118473 A118635

Adjacent sequences: A070977 A070978 A070979 * A070981 A070982 A070983

Keyword

nonn

Author

Benoit Cloitre and Boris Gourevitch (boris(AT)pi314.net), May 17 2002

Extensions

Corrected and extended by Harvey P. Dale, Feb 15 2014

Status

approved