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A243512 Least index i for which A243473(i)=n, or 0 if no such index exists. 2
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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A103851 A024030 A221231 * A165163 A153658 A073785
KEYWORD
nonn
AUTHOR
M. F. Hasler, Jun 05 2014
EXTENSIONS
a(42)-a(67) from Charles R Greathouse IV, Jun 05 2014
STATUS
approved

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Last modified March 4 02:53 EST 2024. Contains 370522 sequences. (Running on oeis4.)