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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 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

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