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A143215 a(n) = prime(n) * Sum_{i=1..n} prime(i). 4
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 (list; graph; refs; listen; history; text; internal format)
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
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
CROSSREFS
Cf. A007504.
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.
Sequence in context: A056337 A053406 A225265 * A301973 A132308 A026110
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Jul 30 2008
EXTENSIONS
More terms from Vladimir Joseph Stephan Orlovsky, Sep 21 2009
STATUS
approved

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Last modified March 28 16:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)