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

1,1

Links

Table of n, a(n) for n=1..44.

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

Example

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

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 *)

Prog

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

Crossrefs

A distant relative of A054640.

Cf. A000203, A001043, A006094, A126199.

Sequence in context: A367105 A270257 A367361 * A081808 A369798 A260261

Adjacent sequences: A180614 A180615 A180616 * A180618 A180619 A180620

Keyword

nonn

Author

Thomas Kellar, Sep 12 2010

Extensions

More terms from Vincenzo Librandi, Feb 16 2015

Name simplified by Omar E. Pol, Dec 08 2019

Status

approved