cp's OEIS Frontend

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

%I A334880 #51 Apr 21 2021 03:55:42
%S A334880 2,5,6,7,10,12,14,15,16,18,20,21,22,24,26,28,30,32,34,36,42,48,50,51,
%T A334880 52,54,55,56,60,62,63,64,65,70,72,74,75,76,77,78,80,81,82,93,96,98,99,
%U A334880 102,104,105,110,112,114,120,122,124,126,128,130,132,138,148
%N A334880 Numbers k such that gcd(k, k-th composite number) > 1.
%H A334880 Harvey P. Dale, <a href="/A334880/b334880.txt">Table of n, a(n) for n = 1..1000</a>
%e A334880 In the following table, c(k) = A002808(k) = k-th composite number.
%e A334880   k     c(k)   gcd(k, c(k))
%e A334880   1      4         1
%e A334880   2      6         2
%e A334880   3      8         1
%e A334880   4      9         1
%e A334880   5     10         5
%e A334880   6     12         6
%e A334880 2, 5, 6 are in this sequence, and 1,3,4 are in A073258.
%t A334880 c = Select[Range[2, 150], ! PrimeQ[#] &]; (* A002808 *)
%t A334880 Select[Range[Length[c]], GCD[c[[#]], #] > 1 &]  (* A334880 *)
%t 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 *)
%o A334880 (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
%Y A334880 Cf. A002808, A064814, A073258 (complement), A336323.
%K A334880 nonn,easy
%O A334880 1,1
%A A334880 _Clark Kimberling_, Jul 17 2020