|
|
A074748
|
|
Numbers for which the differences between consecutive anti-divisors (ordered by size) are not distinct.
|
|
1
|
|
|
15, 17, 20, 22, 28, 30, 32, 37, 38, 39, 43, 45, 52, 53, 58, 59, 62, 67, 73, 75, 77, 82, 85, 87, 88, 90, 94, 95, 97, 98, 99, 105, 111, 115, 118, 120, 122, 123, 124, 127, 128, 135, 137, 138, 142, 143, 145, 148, 149, 150, 157, 158, 162, 171, 172, 173, 175, 178, 179, 181, 182, 185, 188, 189, 193, 195
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
See A066272 for definition of anti-divisor.
|
|
LINKS
|
|
|
EXAMPLE
|
For n=15, anti-divisors={2,6,10}; differences={4,4}, which are not distinct, so 15 is in the sequence.
|
|
MATHEMATICA
|
ad[n_Integer] := Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]; s = ad /@ Range@ 200 /. {{} -> {0, 1}, {_} -> {0, 1}}; Flatten@ Position[Differences /@ s, l_List /; Length@ l != Length@ DeleteDuplicates@ l] (* Michael De Vlieger, Apr 30 2015 *)
|
|
PROG
|
(Python) # See Consiglio link.
(PARI) ad(n)=my(v=List(), r=2^valuation(2*n, 2)); fordiv(2*n-1, d, if(d>1 && d<n, listput(v, d))); fordiv(2*n+1, d, if(d>1 && d<n, listput(v, d))); fordiv(2*n/r, d, if(r*d<n, listput(v, r*d))); Set(v)
diff(v)=vector(max(0, #v-1), i, v[i+1]-v[i])
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|