A243512 Least index i for which A243473(i)=n, or 0 if no such index exists.

1, 2, 120, 4, 9, 14, 25, 8, 26, 42, 34, 20, 121, 27, 169, 16, 58, 39, 289, 48, 74, 114, 82, 52, 529, 94, 760, 133, 106, 68, 841, 32, 122, 186, 172, 93, 522, 70, 146, 217, 81, 63, 1656, 50, 504, 258, 178, 116, 2209, 75, 194, 231, 202, 80, 2809, 36, 218, 343, 226, 148, 3481, 130, 3721, 64, 332, 164, 108000, 136

Offset

0,2

Comments

Motivated by the observation that some small numbers (2,12,14,18,...) occur only very late in the recently added sequence A243473, but all numbers seem to appear sooner or later. (The definition is completed by "0 if no such index exists" to guarantee well-definedness in absence of a proof, but I conjecture that no such 0 will ever occur.)

Least i such that sigma(i)/i = (k+n)/k for some k. - Michel Marcus, Sep 09 2015

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..629

Example

For n=0, 1 satisfies sigma(1)/1 = 1/1 and 1/1 = (1+0)/1; so a(0)=1.
For n=2, 2 satisfies sigma(2)/2 = 3/2 and 3/2 = (2+1)/2; so a(1)=2.
For n=3, 120 satisfies sigma(120)/120 = 3/1 and 3/1 = (1+2)/1; so a(2)=120.

Mathematica

f[n_] := Block[{r = DivisorSigma[1, n]/n}, Numerator[r] - Denominator@ r]; Table[i = 1; While[f@ i != n, i++]; i, {n, 0, 67}] (* Michael De Vlieger, Sep 09 2015 *)

Prog

(PARI) A243473(n)=my(t=sigma(n, -1)); numerator(t)-denominator(t)
v=vector(77); for(n=2, 108000, t=A243473(n); if(t<=#v && !v[t], v[t]=n)); concat(1, v) \\ Charles R Greathouse IV, Jun 05 2014

Crossrefs

Cf. A000203, A001065, A014567, A017665, A017666, A053813.

Sequence in context: A103851 A024030 A221231 * A165163 A153658 A073785

Adjacent sequences: A243509 A243510 A243511 * A243513 A243514 A243515

Keyword

nonn

Author

M. F. Hasler, Jun 05 2014

Extensions

a(42)-a(67) from Charles R Greathouse IV, Jun 05 2014

Status

approved