

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
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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 welldefinedness 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



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)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



