A143215 a(n) = prime(n) * Sum_{i=1..n} prime(i).

4, 15, 50, 119, 308, 533, 986, 1463, 2300, 3741, 4960, 7289, 9758, 12083, 15416, 20193, 25960, 30561, 38056, 45369, 51976, 62489, 72542, 85707, 102820, 117261, 130192, 146697, 161320, 180009, 218440, 242481, 272356, 295653, 339124, 366477

Offset

1,1

Comments

Row sums of triangle A087112.

Sum of semiprimes (A001358) with greater prime factor prime(n). - Gus Wiseman, Dec 06 2020

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Formula

a(n) = A000040(n) * A007504(n).

Example

The series begins (4, 15, 50, 119, 308,...) since the primes = (2, 3, 5, 7, 11,...) and partial sum of primes = (2, 5, 10, 17, 28,...).
a(5) = 308 = 11 * 28.
a(4) = 119 = sum of row 4 terms of triangle A087112: (14 + 21 + 35 + 49).

Maple

A143215:=n->ithprime(n)*sum(ithprime(i), i=1..n); seq(A143215(n), n=1..50); # Wesley Ivan Hurt, Mar 26 2014

Mathematica

Table[Prime[n]*Sum[Prime[i], {i, n}], {n, 50}] (* Wesley Ivan Hurt, Mar 26 2014 *)

Prog

(Haskell)
a143215 n = a000040 n * a007504 n  -- Reinhard Zumkeller, Nov 25 2012
(PARI) a(n) = prime(n)*vecsum(primes(n)); \\ Michel Marcus, Jun 15 2024
(Magma)
A143215:= func< n | NthPrime(n)*(&+[NthPrime(j): j in [1..n]]) >;
[A143215(n): n in [1..50]]; // G. C. Greubel, Aug 27 2024
(SageMath)
def A143215(n): return nth_prime(n)*sum(nth_prime(j) for j in range(1, n+1))
[A143215(n) for n in range(1, 51)] # G. C. Greubel, Aug 27 2024

Crossrefs

Row sums of A087112.

The squarefree version is A339194, row sums of A339116.

Semiprimes grouped by weight are A338904, with row sums A024697.

Squarefree semiprimes grouped by weight are A338905, with row sums A025129.

Squarefree numbers grouped by greatest prime factor are A339195, with row sums A339360.

A001358 lists semiprimes.

A006881 lists squarefree semiprimes.

A332765 is the greatest semiprime of weight n.

A338898/A338912/A338913 give the prime indices of semiprimes.

A338899/A270650/A270652 give the prime indices of squarefree semiprimes.

Cf. A000040, A001222, A001748, A007504, A014342, A098350, A100484, A168472, A319613, A339003, A339114/A339115.

Sequence in context: A056337 A053406 A225265 * A301973 A132308 A372015

Adjacent sequences: A143212 A143213 A143214 * A143216 A143217 A143218

Keyword

nonn

Author

Gary W. Adamson, Jul 30 2008

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Sep 21 2009

Status

approved