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A243932
Positive integers with the same number of twin divisors as non-twin divisors.
2
6, 8, 21, 27, 33, 35, 39, 40, 45, 51, 57, 69, 72, 75, 87, 93, 96, 105, 111, 123, 129, 141, 143, 159, 168, 177, 183, 189, 201, 213, 219, 237, 249, 252, 264, 267, 291, 297, 303, 309, 312, 321, 323, 327, 339, 381, 393, 399, 411, 417, 420, 429, 447, 453, 471, 483, 489, 501
OFFSET
1,1
COMMENTS
A divisor m of n is twin if the positive values of m - 2 and/or m + 2 also divides n.
A divisor k of n is non-twin if the positive values of neither k - 2 nor k + 2 divide n.
LINKS
FORMULA
A243865(a(n)) = A243917(a(n)).
EXAMPLE
The divisors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. Of these, 2, 4, 8, 10, are twin divisors and 1, 5, 20, 40 are non-twin divisors. These are the same number of twin divisors (4) as non-twin divisors (4), so 40 is in this sequence.
MATHEMATICA
fQ[n_] := Block[{d = Divisors@ n}, Length@ d == 2Length@ Select[d, MemberQ[d, # + 2] || MemberQ[d, # - 2] &]]; Select[ Range@ 520, fQ] (* Robert G. Wilson v, Jun 22 2014 *)
PROG
(PARI)
isOK(n) = t=sumdiv(n, d, (d>2 && n%(d-2)==0) || (d<=n-2 && n%(d+2)==0)); if(t==numdiv(n)-t, 1, 0)
s=[]; for(n=1, 600, if(isOK(n), s=concat(s, n))); s \\ Colin Barker, Jun 30 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Missing term (168) inserted by Colin Barker, Jun 30 2014
STATUS
approved