cp's OEIS Frontend

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

%I A143215 #37 Aug 27 2024 04:27:17
%S A143215 4,15,50,119,308,533,986,1463,2300,3741,4960,7289,9758,12083,15416,
%T A143215 20193,25960,30561,38056,45369,51976,62489,72542,85707,102820,117261,
%U A143215 130192,146697,161320,180009,218440,242481,272356,295653,339124,366477
%N A143215 a(n) = prime(n) * Sum_{i=1..n} prime(i).
%C A143215 Row sums of triangle A087112.
%C A143215 Sum of semiprimes (A001358) with greater prime factor prime(n). - _Gus Wiseman_, Dec 06 2020
%H A143215 Reinhard Zumkeller, <a href="/A143215/b143215.txt">Table of n, a(n) for n = 1..1000</a>
%F A143215 a(n) = A000040(n) * A007504(n).
%e A143215 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,...).
%e A143215 a(5) = 308 = 11 * 28.
%e A143215 a(4) = 119 = sum of row 4 terms of triangle A087112: (14 + 21 + 35 + 49).
%p A143215 A143215:=n->ithprime(n)*sum(ithprime(i), i=1..n); seq(A143215(n), n=1..50); # _Wesley Ivan Hurt_, Mar 26 2014
%t A143215 Table[Prime[n]*Sum[Prime[i], {i, n}], {n, 50}] (* _Wesley Ivan Hurt_, Mar 26 2014 *)
%o A143215 (Haskell)
%o A143215 a143215 n = a000040 n * a007504 n  -- _Reinhard Zumkeller_, Nov 25 2012
%o A143215 (PARI) a(n) = prime(n)*vecsum(primes(n)); \\ _Michel Marcus_, Jun 15 2024
%o A143215 (Magma)
%o A143215 A143215:= func< n | NthPrime(n)*(&+[NthPrime(j): j in [1..n]]) >;
%o A143215 [A143215(n): n in [1..50]]; // _G. C. Greubel_, Aug 27 2024
%o A143215 (SageMath)
%o A143215 def A143215(n): return nth_prime(n)*sum(nth_prime(j) for j in range(1,n+1))
%o A143215 [A143215(n) for n in range(1,51)] # _G. C. Greubel_, Aug 27 2024
%Y A143215 Row sums of A087112.
%Y A143215 The squarefree version is A339194, row sums of A339116.
%Y A143215 Semiprimes grouped by weight are A338904, with row sums A024697.
%Y A143215 Squarefree semiprimes grouped by weight are A338905, with row sums A025129.
%Y A143215 Squarefree numbers grouped by greatest prime factor are A339195, with row sums A339360.
%Y A143215 A001358 lists semiprimes.
%Y A143215 A006881 lists squarefree semiprimes.
%Y A143215 A332765 is the greatest semiprime of weight n.
%Y A143215 A338898/A338912/A338913 give the prime indices of semiprimes.
%Y A143215 A338899/A270650/A270652 give the prime indices of squarefree semiprimes.
%Y A143215 Cf. A000040, A001222, A001748, A007504, A014342, A098350, A100484, A168472, A319613, A339003, A339114/A339115.
%K A143215 nonn
%O A143215 1,1
%A A143215 _Gary W. Adamson_, Jul 30 2008
%E A143215 More terms from _Vladimir Joseph Stephan Orlovsky_, Sep 21 2009