A334880 Numbers k such that gcd(k, k-th composite number) > 1.

2, 5, 6, 7, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 28, 30, 32, 34, 36, 42, 48, 50, 51, 52, 54, 55, 56, 60, 62, 63, 64, 65, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 93, 96, 98, 99, 102, 104, 105, 110, 112, 114, 120, 122, 124, 126, 128, 130, 132, 138, 148

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

In the following table, c(k) = A002808(k) = k-th composite number.
  k     c(k)   gcd(k, c(k))
  1      4         1
  2      6         2
  3      8         1
  4      9         1
  5     10         5
  6     12         6
2, 5, 6 are in this sequence, and 1,3,4 are in A073258.

Mathematica

c = Select[Range[2, 150], ! PrimeQ[#] &]; (* A002808 *)
Select[Range[Length[c]], GCD[c[[#]], #] > 1 &]  (* A334880 *)
Module[{nn=200, cmps, len}, cmps=Select[Range[nn], CompositeQ]; len=Length[ cmps]; Select[Thread[{Range[len], cmps}], GCD@@#>1&]][[All, 1]] (* Harvey P. Dale, Sep 20 2020 *)

Prog

(PARI) lista(nn) = {my(n=0, list=List()); forcomposite (c=1, nn, n++; if (gcd(n, c) > 1, listput(list, n))); Vec(list); } \\ Michel Marcus, Jul 19 2020

Crossrefs

Cf. A002808, A064814, A073258 (complement), A336323.

Sequence in context: A286751 A293278 A087791 * A285032 A002157 A050002

Adjacent sequences: A334877 A334878 A334879 * A334881 A334882 A334883

Keyword

nonn,easy

Author

Clark Kimberling, Jul 17 2020

Status

approved