VOOZH about

URL: https://oeis.org/A074748

⇱ A074748 - OEIS

login
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
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
KEYWORD
nonn
AUTHOR
Jason Earls, Sep 06 2002
EXTENSIONS
More terms from David Consiglio, Jr., Apr 28 2015
STATUS
approved