A196527 Greatest common divisor of sums of first n prime numbers and first n composite numbers.

2, 5, 2, 1, 1, 1, 1, 1, 2, 1, 4, 1, 7, 1, 8, 1, 1, 1, 1, 1, 8, 7, 1, 1, 1, 3, 2, 1, 4, 3, 1, 1, 28, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 1, 26, 1, 2, 1, 1, 1, 2, 1, 6, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 1, 1, 10, 1, 2, 1, 1, 1, 1, 3, 8

Offset: 1

Author

Reinhard Zumkeller, Oct 03 2011

Keywords

• nonn

Comments

a(n) = gcd(A007504(n),A053767(n));

a(A196528(n)) = n and a(m) <> n for m < A196528(n).

Examples

			a(1) = gcd(2,4) = 2;
a(2) = gcd(2+3,4+6) = gcd(5,10) = 5;
a(3) = gcd(2+3+5,4+6+8) = gcd(10,18) = 2;
a(4) = gcd(2+3+5+7,4+6+8+9) = gcd(17,19) = 1.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A196529.

Programs

Mathematica

Module[{nn=90,pr,cmp},pr=Accumulate[Prime[Range[nn]]];cmp=Accumulate[ Take[Select[Range[2nn],CompositeQ],nn]];GCD@@#&/@Thread[{pr,cmp}]] (* Harvey P. Dale, Jul 29 2017 *)