A180617 Sum of divisors of the product of two consecutive primes.

12, 24, 48, 96, 168, 252, 360, 480, 720, 960, 1216, 1596, 1848, 2112, 2592, 3240, 3720, 4216, 4896, 5328, 5920, 6720, 7560, 8820, 9996, 10608, 11232, 11880, 12540, 14592, 16896, 18216, 19320, 21000, 22800, 24016, 25912, 27552, 29232, 31320, 32760, 34944, 37248, 38412

Offset: 1

Author

Thomas Kellar, Sep 12 2010

Keywords

• nonn

Examples

			a(1) = sigma(2*3) = 12, a(2) = sigma(3*5) = 24.
		

Crossrefs

A distant relative of A054640.

Cf. A000203, A001043, A006094, A126199.

Programs

Magma

[(1+NthPrime(n))*(1+NthPrime(n+1)): n in [1..50]]; // Vincenzo Librandi, Feb 16 2015

Mathematica

DivisorSigma[1,#]&/@(Times@@@Partition[Prime[Range[50]],2,1]) (* Harvey P. Dale, Apr 04 2015 *)
Table[Prime[n]*Prime[n+1]+Prime[n]+Prime[n+1]+1,{n,1,30}] (* Metin Sariyar, Dec 08 2019 *)

PARI

for (n=1,10, i=prod(x=n,n+1,prime(x)); p=sigma(i); print1(p, ", "); )

PARI

a(n)=my(p=prime(n)); (p+1)*(nextprime(p+1)+1) \\ Charles R Greathouse IV, Feb 16 2015

Formula

a(n) = A000203(A006094(n)). - Omar E. Pol, Dec 08 2019

a(n) = A006094(n) + A001043(n) + 1. - Metin Sariyar, Dec 08 2019

a(n) = A126199(n) + 1 (after above formula). - Omar E. Pol, Dec 08 2019

Extensions

More terms from Vincenzo Librandi, Feb 16 2015

Name simplified by Omar E. Pol, Dec 08 2019