A074748 Numbers for which the differences between consecutive anti-divisors (ordered by size) are not distinct.

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

Offset

1,1

Comments

See A066272 for definition of anti-divisor.

Links

David Consiglio, Jr. and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 288 terms from Consiglio)

David Consiglio, Jr., Python program (2015)

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])
is(n)=my(v=diff(ad(n))); #Set(v)<#v \\ Charles R Greathouse IV, Apr 28 2015

Crossrefs

Cf. A066272.

Sequence in context: A043669 A043704 A329177 * A183981 A155111 A124334

Adjacent sequences: A074745 A074746 A074747 * A074749 A074750 A074751

Keyword

nonn

Author

Jason Earls, Sep 06 2002

Extensions

More terms from David Consiglio, Jr., Apr 28 2015

Status

approved