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

1,1

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

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

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

Cf. A134321, A243865, A243917.

Sequence in context: A083595 A064840 A306379 * A242504 A267023 A084962

Adjacent sequences: A243929 A243930 A243931 * A243933 A243934 A243935

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jun 15 2014

Extensions

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

Status

approved