A243932 Positive integers with the same number of twin divisors as non-twin divisors.

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

Author

Juri-Stepan Gerasimov, Jun 15 2014

Keywords

• nonn

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.

Examples

			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.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A134321, A243865, A243917.

Programs

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 *)

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

Formula

A243865(a(n)) = A243917(a(n)).

Extensions

Missing term (168) inserted by Colin Barker, Jun 30 2014