A274382 a(n) = gcd(n, n*(n+1)/2 - sigma(n)).

1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 6, 1, 4, 1, 1, 1, 24, 1, 1, 1, 14, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 10, 1, 3, 1, 2, 3, 1, 1, 4, 1, 2, 3, 4, 1, 3, 1, 4, 1, 1, 1, 6, 1, 1, 1, 1, 1, 3, 1, 4, 3, 1, 1, 3, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 14, 1, 1

Offset: 1

Author

Paolo P. Lava, Jun 23 2016

Keywords

• nonn
• easy

Examples

			a(6) = 3 because 6*7/2 - sigma(6) = 21 - 12 = 9 and gcd(6,9) = 3.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A009194, A024816.

Programs

Magma

[GCD(n, n*(n+1) div 2-SumOfDivisors(n)): n in [1..100]]; // Vincenzo Librandi, Jun 25 2016

Maple

with(numtheory); P:=proc(q) local n;
for n from 1 to q do print(gcd(n,n*(n+1)/2-sigma(n))); od; end: P(10^3);

Mathematica

Table[GCD[n, n (n+1)/2 - DivisorSigma[1, n]], {n, 100}] (* Vincenzo Librandi, Jun 25 2016 *)

PARI

a(n) = gcd(n, n*(n+1)/2-sigma(n)) \\ Felix Fröhlich, Jun 23 2016

Formula

a(n) = gcd(n, A000217(n)-A000203(n)). - Felix Fröhlich, Jun 23 2016

a(n) = gcd(n, antisigma(n)) = gcd(n, A024816(n)). - Omar E. Pol, Jun 29 2016