A346644 Least k >= 1 such that sigma(k)/tau(k) has denominator n or zero if no k exists.

1, 2, 4, 8, 16, 450, 64, 128, 36, 162, 1024, 1800, 4096, 1458, 144, 32768, 65536, 54450, 262144, 405000, 576, 118098, 4194304, 28800, 1296, 1062882, 900, 5832, 268435456, 115200, 1073741824, 2147483648, 9216, 86093442, 5184, 217800, 68719476736, 774840978, 102400

Offset

1,2

Comments

Conjecture: k always exists.

Links

Table of n, a(n) for n=1..39.

Mathematica

seq[max_] := Module[{s = Table[0, {max}], c = 0, n = 1}, While[c < max, d = Denominator[DivisorSigma[1, n]/DivisorSigma[0, n]]; If[d <= max && s[[d]] == 0, c++; s[[d]] = n]; n++]; s]; seq[22] (* Amiram Eldar, Jul 26 2021 *)

Prog

(PARI) a(n)=if(n<0, 0, t=1; while(denominator(sigma(t)/numdiv(t))!=n, t++); t)

Crossrefs

Cf. A057020, A057021, A069081.

Sequence in context: A061581 A046251 A281291 * A164312 A068806 A090804

Adjacent sequences: A346641 A346642 A346643 * A346645 A346646 A346647

Keyword

nonn

Author

Benoit Cloitre, Jul 26 2021

Extensions

a(29)-a(36) from Amiram Eldar, Jul 26 2021

a(37) from David A. Corneth, Jul 26 2021

a(38)-a(39) from Jinyuan Wang, Jul 26 2021

Status

approved